EXAMPLE QUESTIONS ON PERCENTAGES
Question 1: When 75 is added to 75% of a number, the answer is the number. Find 40% of that number.
(a) 100
(b) 80
(c) 120
(d) 160
Answer and Explanations
The right answer is option c
Let the number be p.
75% of p + 75 = p
⇒(75/100)p + 75 = p
⇒ 75 = p –(75p/100)
⇒ 75 =(25p/100)
⇒ p= 75 × 4 = 300
∴ 40% of p =(40/100) × 300 = 120.
Question 2: If 40% of A is added to 50% of B, the answer is 80% of B. What percentage of B is A?
(a) 30%
(b) 40%
(c) 70%
(d) 75%
Answer and Explanations
Option D is the right answer
(A*0.4)+(B*0.5)=(B*0.8)
(A*0.4)=(B*0.8)-(B*0.5)
(A*0.4)=(B*O.3)
A= 3/4 OF B
A= 75% of B
Question 3: If 50% of (x – y) = 30% of (x + y), then what per cent of x is y?
(a) 25%
(b) 100/3 %
(c) 40%
(d) 400%
Answer and Explanations
option (a)is correct
given 50% of(x-y)=30% of(x-y)
(x-y)/2=0.3(x-y)
5(x-y)=3(x+y)
5x-3x=3y+5y
2x=8y
y= x/4
y/x=1/4(100) =25%
Question 4: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had
(a) 588 apples
(b) 600 apples
(c) 672 apples
(d) 700 apples
Answer and Explanation
The right option is option d
Let the fruit seller originally have y apples.
According to the question,
Total apples – sold apples = left apples
y – 40% of y = 420
y – (40/100)x y = 420
y – (2y/5) = 420
{(5y – 2y)/5} = 420
3y/5 = 420
y =(420 x 5)/3 = 700
Question 5: If a% of a is 9, then ‘a’ is equal to
(a) 300
(b) 400
(c) 30
(d) 20
Answer and Explanation
The right answer is option c
Given, a% of a = 9
(a/100) x a = 9
⇒ a^2 = 900
therefore a= 30
Question 6. Two friends, Akash & Beenu had some candies each. One of them had 15 candies more than the other. The candies with Akash was 60% of the total candies with them. How many candies did each have?
A. 40, 25 B. 47, 32 C. 45, 30 D. 49, 34
Answer and explanation
Option C
Let the candies with be (x + 15) and x.
Therefore, x + 15 = 60/100(x + 15 + x)
(x + 15) = 3/5(2x + 15)
5x + 75 = 6x + 45
x = 30
So, the marks of two students are 45 and 30.
Question 7. A fruit seller had some oranges. He sells 30% oranges and still has 140 mangoes. Originally, he had:
A. 288 oranges
B. 300 oranges
C. 672 oranges
D. 200 oranges
Answer and explanation
Option D
Suppose originally he had x oranges.
Then, (100 - 30)% of x = 140.
70/100 x = 140
x = (140 x 100)/70 = 200.
Question 8. What percentage of numbers from 1 to 30 has 1 or 9 in the unit's digit?
A. 12
B. 15
C. 20
D. 22
Answer and explanation
Option C
Such numbers from 1 to 30 are 1, 9, 11, 19, 21, 29
Number of such numbers =6
Required percentage is (6/30 * 100) % = 20%
Question 9. If M = y% of z and B = z% of y, then which of the following must be true?
A. M is lesser than N.
B. M is more than N
C. Relation between M and N cannot be determined.
D. None of these
Answer and explanation
Option D
y% of z = (y/100 x z) = (z/100 x y) = z% of y
A = B.
5. In ABC College, 63% of students are less than 20 years of age. The number of students more than 20 years of age is 2/3 of number of students of 20 years of age which is 42. What is the total number of students in the ABC College?
A. 75
B. 90
C. 130
D. 200
Answer and explanation
Option D
Let the total number of students be x.
Then, Number of students more than 20 years of age = (100 - 63)% of x = 37% of x.
37% of x = 42 + 2/3 of 48
37/100x = 74
x = 200
Question 11. Satish is 20 % heavier than Bhaskar in weight. By how much percent is Rekha lighter than Soni?
A. 20%
B. 25%
C. 16.67%
D. None of these
Answer abd Explanation
Option C
Required % = 100 * 20/ 120 = 16.67 %. (Applying: 100 * R/(100 + R))
Question 12. In a class of 72 students, 87.5 % of the students cleared the GATE exam. How many did not clear it?
A. 12
B. 9
C. 18
D. None of these
Answer and Explanation
Option B
Numbers of students who did not clear the GATE exam = 12.5 * 72/100 = 9.
Question 13. The population of a town increases at the rate of 3.7 % each year. It is 31,110 now. What was it last year?
A. 30,000
B. 29,959
C. 30,270
D. None of these
Answer and Explanation
Option A
Last year it was x
31110 = x (1 + 3.7/100) ⇒ x = 30000.
Question 14. When the cost of cigarettes increases by 25 %, a man reduces his annual consumption by 10 %. Find the % change in his annual expenditure on cigarettes?
A. 12.5 %
B. 11.11 %
C. 15 %
D. 6.25 %
Answer and explanation
Option A
% change in the annual expenditure = 1.25 * 0.9 = 1.125
⇒ Net increase of 12.5 %
Question 15. The tax on an article is increased by 20 %. As a result of which the consumption decreases by 25 %. What is the % change in the tax revenue received by the government from this article?
A. 10 % decrease
B. 15 % increase
C. 10 % increase
D. None of these
Answer and Explanation
Option A
%change in revenue= +20-25+((20*(-25))/100)
-5-5=-10% Net decreased of 10%
Question.16. Mounika spends 35 % of her income on clothes and 40 % on food. If food amounts to Rs. 384, what does she spend on clothes (in Rs.)?
A. 436
B. 320
C. 310
D. None of these
Answer and Explanation
Option D
Let her total income = x %; 40x/100 = 384 ⇒ x = 960.
Hence amount spent on clothes = 960 * 35/100 = 336.
Question.17.Devika required Rs. 800 for paying her fees. She borrowed 20 % from her brother and 30 % of the remaining was funded by her mother. In her bank she had Rs. 200. How much more does she need (in Rs.)?
A. 248
B. 336
C. 148
D. 236
Answer and Explanation
Option A
Required amount = 800
From her brother she got = 800 x 20/100 = 160
From her mother she got = (800-160) * 30/100 = 640 * 30/100 = 192
From the Bank she got Rs. 200
∴ Now she needs 800 - (160 + 192 + 200)
= 800 - 552 = Rs. 248 more
Question 18. Rakesh the barber shaved 40 % of his customers and gave a haircut to 80 % of his customers.
He charged Rs. 7 for a shave and Rs. 5 for a haircut. If 20 % of customers who opted for a shave also had
a hair-cut, what were Rakesh earnings if he had 75 customers (in Rs.)?
A. 410
B. 1,020
C. 510
D. None of these
Answer and Explanation
Option C
Total customers = 75
Numbers of customers shaved = 75 * 40/100 = 30
Number of customers who got hair cut = 75 * 80/100 = 60
∴ His total income= (30 * 7) + (60 * 5) = 210 + 300 = 510.
Question19. Sudhir ate 20 % of the bananas and 30 % of the apples. If there were 40 bananas and 20 apples, how many fruits did he eat?
A. 18
B. 15
C. 16
D. 14
Answer and explanation
Option D
Sudhir ate 40 * 20/100 + 20 * 30/100 = 8 + 6 = 14.
Question20. karthiek gave his sister 40 % of his pocket money and was left with Rs. 8. What is his pocket money (in Rs.)?
A. 20
B. 13.33
C. 11.20
D. 12.80
Answer and Explanation
option B
He gave his sister 40 % i.e. he is left with 60 % of the total money which is Rs. 8. Hence 60x/100 = 8 ⇒ x = 13.33.
Question21. A student obtained 62.5 % marks in a certain examination. If the maximum marks are 800. Find the total marks obtained by her.
A. 525
B. 600
C. 375
D. 500
Answer and Explanation
Option C
Solution: 800 * 62.5/100 = 500
Question22. The annual sales of company B were Rs 96,000 in fiscal year 95-96 and Rs 1,08,000 in fiscal 96-97. What was the % increase in turnover?
A. 16.67 %
B. 62.5 %
C. 40 %
D. 12.5 %
Answer and explanation
Option D
Solution: Increase = 96,000 – 1,08, 000 = 12,000
∴ % Increase = 12000 * 100/96000 = 100 * 1/8 = 12.5 \
Question33. The price of a Bajaj Scooter is Rs 25,000 which is 20 % lesser than a LML Scooter. What is the price of a LML Scooter?
A. 15250
B. 31250
C. 40150
D. 75230
Answer and Explanation
Option B
Solution: Here note that the % given is defined in terms of the price of LML Scooter and not Bajaj Scooter. ∴ Computing the price of SMS as 1.2 times Bajaj's price will give incorrect answer. The data given is:
LML * (100 – 20)/100 = Bajaj = 25,000
∴ LML =25,000 × 100/80 = Rs 31,250
Or you can simply do = 25,000/0.8 = 31250
(20 % less means it is 0.80 times of the other one)
Question24. The price of rice increases by 30 %. In order to keep the expenses on rice constant as before, by what percentage should a person cut down his consumption?
A. 22/3 %
B. 31/5 %
C. 67/3 %
D. 23/11 %
Answer and Explanation
Option C
Solution: Applying the formula 100 * R/ (100 + R),
Since the price has increased, the consumption should be reduced by:
(100 * 30)/ (100+130) = 22 1/3 %
Question 25. Tom’s income is 20 % less than Jerry’s. How much is Jerry’s income more than Tom’s?
A. 25 %
B. 60 %
C. 45 %
D. 30 %
Answer and explanation
Option A
Solution: Applying the formula 100 * R/(100 - R)
As , income is 20% less
Jerry’s income is more by = 100 * 20/80 = 25 %
Question 26. A traveling salesman carried 75 % of his money in traveler’s cheque and 25 % in cash. During one of his journeys, he lost his entire cash and spent from his traveler’s cheque. On completion of the journey, he returned 30% of the traveler’s cheque, which amounted to Rs 180. What was the total money that he carried?
A. Rs 500
B. Rs 600
C. Rs 450
D. Rs 800
Answer and explanation
Option D
Solution: 30 % of Traveler’s Cheque = Rs 180
∴ 100 % of Traveler's Cheque = 180 * 100/30 = Rs 600
Since Traveler's Cheque accounted for 75% of the total money that he had carried, the total money that he carried is: 600 * 100/75 = Rs 800
Question 27. A number is increased by 20%, and then it is decreased by 30%, what is the net change in the number?
A. 16 % increase
B. 16 % decrease
C. 10 % decrease
D. 5 % increase
Answer and Explanation
Option B
Solution: Using the formula: X + Y + XY/100
⇒ 20 + (-30) + 20 *-30 /100 = -16
This means there is a decrease of 16 %
Question 28. A square is converted into a rectangle by increasing one of its sides by 5 % and reducing the other by 5 %. What will be the % change in the area of the two figures?
A. 0.5 % decrease
B. 0.5 % increase
C. 0.25 % increase
D. 0.25 % decrease
Answer and questions
Option D
Solution: Let the side of the square = a
∴ Its area = a^2; When the square is being converted to a rectangle, the length becomes 1.05a and the width becomes 0.95a. ∴ New area = 1.05a × 0.95a = 0.9975a^2
Change in area = a decrease of 0.0025a^2
∴ % decrease in area =0.0025a^2 * 100/a^2= 0.25 %
Question 29. In an election there were two candidates P and S. The poll turnout was only 90 %. 500 of the given votes were declared invalid. P won by a margin of 400 votes and got 440/9 % of the total votes. Find the total number of eligible voters and the number of votes received by each of the candidates.
A. 5000,2200,1800
B. 6000,1200,3800
C. 4000,1100,3500
D. 4500,2200,1000
Answer and Explanation
Option A
Solution: Let the registered voters = X
P got 440/9 % of X = 440/9 % of X = 4.49X/9
Since P got 400 votes more than S, S got 4.4X/9 – 400
Total votes registered = X = P + S + Invalid votes
X = 4.4 X/9 + (4.4 X/9 – 400)+ 500 ⇒ X = 8.8X/9 + 100
⇒ X = 4500. Since the poll turnout was only 90%, the total number of eligible voters = 100/90 * 4500 = 5000
Number of votes P got = 4.4/9 * 4500 = 2200
Number of votes S got = 2200 – 400 = 1800.
Question 30. If the population of a town is 926100 and it has been growing annually at 5 %, what was the population 3 years ago?
A. 200,000
B. 600,000
C. 400,000
D. 450,000
Answer and Explanation
Option A
Let the population be X
X * (100 + 5)3 / (100) 3 =926100 %rArr; X * (105/ 100) * (105/100) * (105/100) = 926100
⇒ X * (21/20) * (21/20) * (21/20) = 926100
⇒ X = 926100 * (20/21) * (20/21) * (20/21) = 8, 00, 00
31. The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
A. 20%
B. 18%
C. 15%
D. 12%
Answer and Explanation
option D
Using the formula: X + Y + XY/100
-20+10+(-200/100) = -10-2 = -12(- indicates decrease)
32. At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
A. 70%
B. 90%
C. 80%
D. 75%
Answer & Explanation
Answer: Option C
Explanation:
A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
33. If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
A. 1,20,000
B. 1,10,000
C. 1,00,000
D. 90,000
Answer & Explanation
Answer: Option A
Explanation:
X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
34. There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
A. 456
B. 744
C. 912
D. 1200
Answer & Explanation
Answer: Option B
Explanation:
W = 62% L = 38%
62% - 38% = 24%
24% -------- 288(1%= 288/24 =12)
62% -------- ? => 744(62*744)
35. Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
A. Nothing
B. 10%
C. 1%
D. 5%
Answer & Explanation
Answer: Option C
Using the formula: X + Y + XY/100
-10+10+((-10*10)/100)= 1%
36. A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
A. Rs.3600
B. Rs.4000
C. Rs.4500
D. Rs.3000
Answer & Explanation
Answer: Option A
Explanation:
X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
37. The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females?
A. 60%
B. 50%
C. 45%
D. 40%
Answer & Explanation
Answer: Option B
Explanation:
Male = 45,000* 5/9 = 25,000
Female = 45,000* 4/9 = 20,000
Married Male = 25,000* 40/100 = 10,000
Married Female = 10,000
20,000 ------------ 10,000
100 ------------- ? => 50%
38. The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
A. 90% increase
B. 45% increase
C. 9% decrease
D. Same as before
Answer & Explanation
Answer: Option C
Using the formula: X + Y + XY/100
39. In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A. 173
B. 163
C. 153
D. 143
Answer & Explanation
Answer: Option C
Explanation:
44 + 28 + 10 = 82%
100 – 82 = 18%
850 * 18/100 = 153
40. When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
A. 133 1/3 m
B. 150 m
C. 106 2/3 m
D. 166 2/3 m
Answer & Explanation
Answer: Option D
Explanation:
5% - 2% = 3%
3% ---- 5(20 million bag - 15 million bag)
100% ---- ? => 166 2/3
41. If P gets 25% more than Q, then by what percent does Q get less than P?
A. 33 1/3%
B. 30%
C. 20%
D. 16 2/3%
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
Let Q get 1 unit.
25% of 1 unit = 1/4 = 0.25
P gets (1 + 0.25) i.e., 1.25 units.
Difference = (1.25 - 1) = 0.25
Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20%
42.At the special sale,5 tickets can be puchased for he price of 3 tickets.If 5 tickets are purchased at the sale, the amount saved will be what percent of
the orignal price of the 5 tickets?
A.20%
B.33 1/2%
C.40%
D.60%
Answer and Explanation
Answer: option C
Explanation:
let the initial price of each ticket be Rs.100
Then,orignal price of 5 tickets is Rs500
sale price of 5 tickets is Rs300
Amount saved=Rs(500-300)=200
Required percentage =((200/500)*100)=40%
43.solve[180% of (?)]/2=504
A.400
B.480
C.560
d.600
Answer and Explanation
option C
Explanation:
X*0.18=1008
X=1008*100/180=560
44.In a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?
A) 324138 B) 349680
C) 509940 D) None of these
Answer & ExplanationAnswer: A) 324138
Explanation:
Total Population = 728400
Migrants = 35 % of 728400 = 254940
local population = (728400 - 254940) = 473460.
Rural migrants = 20% of 254940 = 50988
Urban migrants = (254940 - 50988) = 203952
Female population = 48% of 473460 + 30% of 50988 + 40% of 203952 = 324138
45.n a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?
A) 4000 B) 8000
C) 12000 D) 16000
Answer & ExplanationAnswer: B) 8000
Explanation:
Let the number of candidates appeared from each state be x.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
46.A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets ?
A) 40% B) 45%
C) 50% D) 55%
Answer & ExplanationAnswer: C) 50%
Explanation:
Number of runs made by running = 120 - (3 x 4 + 8 x 6) = 120 - (60) = 60
Required percentage = [(60/120)*100] % = 50%
47.A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A) 0.75D B) 0.76D
C) 0.765D D) None of the above
Answer & ExplanationAnswer: C) 0.765D
Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
48.Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ?
A) 10.769 % B) 11.23 %
C) 10.4 % D) 9.87 %
Answer & ExplanationAnswer: A) 10.769 %
Explanation:
I II III
65 58 100
65 -------- 7
100 ------ ? => 10.769%
49.Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
A) 0.15% B) 15%
C) 0.125% D) None of these
Answer & ExplanationAnswer: D) None of these
Explanation:
Total land of Sukhiya = 480x/0.6 = 800x
Cultivated land of village = 384000x
Required percentage = 800x/384000x 100 = 0.20833
50.A Shopkeeper charges sales tax of x% upto Rs.2,000 and above it he charges y%. A customer pays total tax of Rs 320, when he purchases the goods worth Rs. 6,000 and he pay's the total tax of Rs. 680 for the goods worth Rs. 12,000. The value of (x-y) is:
A) 0 B) -2
C) -4 D) 5
Answer & ExplanationAnswer: B) -2
Explanation:
2000xX/100 + 4000xY/100 = 320
and 2000xX/100 + 10000xY/100 = 680
x = 4 and y = 6
x-y = -2
Question 1: When 75 is added to 75% of a number, the answer is the number. Find 40% of that number.
(a) 100
(b) 80
(c) 120
(d) 160
Answer and Explanations
The right answer is option c
Let the number be p.
75% of p + 75 = p
⇒(75/100)p + 75 = p
⇒ 75 = p –(75p/100)
⇒ 75 =(25p/100)
⇒ p= 75 × 4 = 300
∴ 40% of p =(40/100) × 300 = 120.
Question 2: If 40% of A is added to 50% of B, the answer is 80% of B. What percentage of B is A?
(a) 30%
(b) 40%
(c) 70%
(d) 75%
Answer and Explanations
Option D is the right answer
(A*0.4)+(B*0.5)=(B*0.8)
(A*0.4)=(B*0.8)-(B*0.5)
(A*0.4)=(B*O.3)
A= 3/4 OF B
A= 75% of B
Question 3: If 50% of (x – y) = 30% of (x + y), then what per cent of x is y?
(a) 25%
(b) 100/3 %
(c) 40%
(d) 400%
Answer and Explanations
option (a)is correct
given 50% of(x-y)=30% of(x-y)
(x-y)/2=0.3(x-y)
5(x-y)=3(x+y)
5x-3x=3y+5y
2x=8y
y= x/4
y/x=1/4(100) =25%
Question 4: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had
(a) 588 apples
(b) 600 apples
(c) 672 apples
(d) 700 apples
Answer and Explanation
The right option is option d
Let the fruit seller originally have y apples.
According to the question,
Total apples – sold apples = left apples
y – 40% of y = 420
y – (40/100)x y = 420
y – (2y/5) = 420
{(5y – 2y)/5} = 420
3y/5 = 420
y =(420 x 5)/3 = 700
Question 5: If a% of a is 9, then ‘a’ is equal to
(a) 300
(b) 400
(c) 30
(d) 20
Answer and Explanation
The right answer is option c
Given, a% of a = 9
(a/100) x a = 9
⇒ a^2 = 900
therefore a= 30
Question 6. Two friends, Akash & Beenu had some candies each. One of them had 15 candies more than the other. The candies with Akash was 60% of the total candies with them. How many candies did each have?
A. 40, 25 B. 47, 32 C. 45, 30 D. 49, 34
Answer and explanation
Option C
Let the candies with be (x + 15) and x.
Therefore, x + 15 = 60/100(x + 15 + x)
(x + 15) = 3/5(2x + 15)
5x + 75 = 6x + 45
x = 30
So, the marks of two students are 45 and 30.
Question 7. A fruit seller had some oranges. He sells 30% oranges and still has 140 mangoes. Originally, he had:
A. 288 oranges
B. 300 oranges
C. 672 oranges
D. 200 oranges
Answer and explanation
Option D
Suppose originally he had x oranges.
Then, (100 - 30)% of x = 140.
70/100 x = 140
x = (140 x 100)/70 = 200.
Question 8. What percentage of numbers from 1 to 30 has 1 or 9 in the unit's digit?
A. 12
B. 15
C. 20
D. 22
Answer and explanation
Option C
Such numbers from 1 to 30 are 1, 9, 11, 19, 21, 29
Number of such numbers =6
Required percentage is (6/30 * 100) % = 20%
Question 9. If M = y% of z and B = z% of y, then which of the following must be true?
A. M is lesser than N.
B. M is more than N
C. Relation between M and N cannot be determined.
D. None of these
Answer and explanation
Option D
y% of z = (y/100 x z) = (z/100 x y) = z% of y
A = B.
5. In ABC College, 63% of students are less than 20 years of age. The number of students more than 20 years of age is 2/3 of number of students of 20 years of age which is 42. What is the total number of students in the ABC College?
A. 75
B. 90
C. 130
D. 200
Answer and explanation
Option D
Let the total number of students be x.
Then, Number of students more than 20 years of age = (100 - 63)% of x = 37% of x.
37% of x = 42 + 2/3 of 48
37/100x = 74
x = 200
Question 11. Satish is 20 % heavier than Bhaskar in weight. By how much percent is Rekha lighter than Soni?
A. 20%
B. 25%
C. 16.67%
D. None of these
Answer abd Explanation
Option C
Required % = 100 * 20/ 120 = 16.67 %. (Applying: 100 * R/(100 + R))
Question 12. In a class of 72 students, 87.5 % of the students cleared the GATE exam. How many did not clear it?
A. 12
B. 9
C. 18
D. None of these
Answer and Explanation
Option B
Numbers of students who did not clear the GATE exam = 12.5 * 72/100 = 9.
Question 13. The population of a town increases at the rate of 3.7 % each year. It is 31,110 now. What was it last year?
A. 30,000
B. 29,959
C. 30,270
D. None of these
Answer and Explanation
Option A
Last year it was x
31110 = x (1 + 3.7/100) ⇒ x = 30000.
Question 14. When the cost of cigarettes increases by 25 %, a man reduces his annual consumption by 10 %. Find the % change in his annual expenditure on cigarettes?
A. 12.5 %
B. 11.11 %
C. 15 %
D. 6.25 %
Answer and explanation
Option A
% change in the annual expenditure = 1.25 * 0.9 = 1.125
⇒ Net increase of 12.5 %
Question 15. The tax on an article is increased by 20 %. As a result of which the consumption decreases by 25 %. What is the % change in the tax revenue received by the government from this article?
A. 10 % decrease
B. 15 % increase
C. 10 % increase
D. None of these
Answer and Explanation
Option A
%change in revenue= +20-25+((20*(-25))/100)
-5-5=-10% Net decreased of 10%
Question.16. Mounika spends 35 % of her income on clothes and 40 % on food. If food amounts to Rs. 384, what does she spend on clothes (in Rs.)?
A. 436
B. 320
C. 310
D. None of these
Answer and Explanation
Option D
Let her total income = x %; 40x/100 = 384 ⇒ x = 960.
Hence amount spent on clothes = 960 * 35/100 = 336.
Question.17.Devika required Rs. 800 for paying her fees. She borrowed 20 % from her brother and 30 % of the remaining was funded by her mother. In her bank she had Rs. 200. How much more does she need (in Rs.)?
A. 248
B. 336
C. 148
D. 236
Answer and Explanation
Option A
Required amount = 800
From her brother she got = 800 x 20/100 = 160
From her mother she got = (800-160) * 30/100 = 640 * 30/100 = 192
From the Bank she got Rs. 200
∴ Now she needs 800 - (160 + 192 + 200)
= 800 - 552 = Rs. 248 more
Question 18. Rakesh the barber shaved 40 % of his customers and gave a haircut to 80 % of his customers.
He charged Rs. 7 for a shave and Rs. 5 for a haircut. If 20 % of customers who opted for a shave also had
a hair-cut, what were Rakesh earnings if he had 75 customers (in Rs.)?
A. 410
B. 1,020
C. 510
D. None of these
Answer and Explanation
Option C
Total customers = 75
Numbers of customers shaved = 75 * 40/100 = 30
Number of customers who got hair cut = 75 * 80/100 = 60
∴ His total income= (30 * 7) + (60 * 5) = 210 + 300 = 510.
Question19. Sudhir ate 20 % of the bananas and 30 % of the apples. If there were 40 bananas and 20 apples, how many fruits did he eat?
A. 18
B. 15
C. 16
D. 14
Answer and explanation
Option D
Sudhir ate 40 * 20/100 + 20 * 30/100 = 8 + 6 = 14.
Question20. karthiek gave his sister 40 % of his pocket money and was left with Rs. 8. What is his pocket money (in Rs.)?
A. 20
B. 13.33
C. 11.20
D. 12.80
Answer and Explanation
option B
He gave his sister 40 % i.e. he is left with 60 % of the total money which is Rs. 8. Hence 60x/100 = 8 ⇒ x = 13.33.
Question21. A student obtained 62.5 % marks in a certain examination. If the maximum marks are 800. Find the total marks obtained by her.
A. 525
B. 600
C. 375
D. 500
Answer and Explanation
Option C
Solution: 800 * 62.5/100 = 500
Question22. The annual sales of company B were Rs 96,000 in fiscal year 95-96 and Rs 1,08,000 in fiscal 96-97. What was the % increase in turnover?
A. 16.67 %
B. 62.5 %
C. 40 %
D. 12.5 %
Answer and explanation
Option D
Solution: Increase = 96,000 – 1,08, 000 = 12,000
∴ % Increase = 12000 * 100/96000 = 100 * 1/8 = 12.5 \
Question33. The price of a Bajaj Scooter is Rs 25,000 which is 20 % lesser than a LML Scooter. What is the price of a LML Scooter?
A. 15250
B. 31250
C. 40150
D. 75230
Answer and Explanation
Option B
Solution: Here note that the % given is defined in terms of the price of LML Scooter and not Bajaj Scooter. ∴ Computing the price of SMS as 1.2 times Bajaj's price will give incorrect answer. The data given is:
LML * (100 – 20)/100 = Bajaj = 25,000
∴ LML =25,000 × 100/80 = Rs 31,250
Or you can simply do = 25,000/0.8 = 31250
(20 % less means it is 0.80 times of the other one)
Question24. The price of rice increases by 30 %. In order to keep the expenses on rice constant as before, by what percentage should a person cut down his consumption?
A. 22/3 %
B. 31/5 %
C. 67/3 %
D. 23/11 %
Answer and Explanation
Option C
Solution: Applying the formula 100 * R/ (100 + R),
Since the price has increased, the consumption should be reduced by:
(100 * 30)/ (100+130) = 22 1/3 %
Question 25. Tom’s income is 20 % less than Jerry’s. How much is Jerry’s income more than Tom’s?
A. 25 %
B. 60 %
C. 45 %
D. 30 %
Answer and explanation
Option A
Solution: Applying the formula 100 * R/(100 - R)
As , income is 20% less
Jerry’s income is more by = 100 * 20/80 = 25 %
Question 26. A traveling salesman carried 75 % of his money in traveler’s cheque and 25 % in cash. During one of his journeys, he lost his entire cash and spent from his traveler’s cheque. On completion of the journey, he returned 30% of the traveler’s cheque, which amounted to Rs 180. What was the total money that he carried?
A. Rs 500
B. Rs 600
C. Rs 450
D. Rs 800
Answer and explanation
Option D
Solution: 30 % of Traveler’s Cheque = Rs 180
∴ 100 % of Traveler's Cheque = 180 * 100/30 = Rs 600
Since Traveler's Cheque accounted for 75% of the total money that he had carried, the total money that he carried is: 600 * 100/75 = Rs 800
Question 27. A number is increased by 20%, and then it is decreased by 30%, what is the net change in the number?
A. 16 % increase
B. 16 % decrease
C. 10 % decrease
D. 5 % increase
Answer and Explanation
Option B
Solution: Using the formula: X + Y + XY/100
⇒ 20 + (-30) + 20 *-30 /100 = -16
This means there is a decrease of 16 %
Question 28. A square is converted into a rectangle by increasing one of its sides by 5 % and reducing the other by 5 %. What will be the % change in the area of the two figures?
A. 0.5 % decrease
B. 0.5 % increase
C. 0.25 % increase
D. 0.25 % decrease
Answer and questions
Option D
Solution: Let the side of the square = a
∴ Its area = a^2; When the square is being converted to a rectangle, the length becomes 1.05a and the width becomes 0.95a. ∴ New area = 1.05a × 0.95a = 0.9975a^2
Change in area = a decrease of 0.0025a^2
∴ % decrease in area =0.0025a^2 * 100/a^2= 0.25 %
Question 29. In an election there were two candidates P and S. The poll turnout was only 90 %. 500 of the given votes were declared invalid. P won by a margin of 400 votes and got 440/9 % of the total votes. Find the total number of eligible voters and the number of votes received by each of the candidates.
A. 5000,2200,1800
B. 6000,1200,3800
C. 4000,1100,3500
D. 4500,2200,1000
Answer and Explanation
Option A
Solution: Let the registered voters = X
P got 440/9 % of X = 440/9 % of X = 4.49X/9
Since P got 400 votes more than S, S got 4.4X/9 – 400
Total votes registered = X = P + S + Invalid votes
X = 4.4 X/9 + (4.4 X/9 – 400)+ 500 ⇒ X = 8.8X/9 + 100
⇒ X = 4500. Since the poll turnout was only 90%, the total number of eligible voters = 100/90 * 4500 = 5000
Number of votes P got = 4.4/9 * 4500 = 2200
Number of votes S got = 2200 – 400 = 1800.
Question 30. If the population of a town is 926100 and it has been growing annually at 5 %, what was the population 3 years ago?
A. 200,000
B. 600,000
C. 400,000
D. 450,000
Answer and Explanation
Option A
Let the population be X
X * (100 + 5)3 / (100) 3 =926100 %rArr; X * (105/ 100) * (105/100) * (105/100) = 926100
⇒ X * (21/20) * (21/20) * (21/20) = 926100
⇒ X = 926100 * (20/21) * (20/21) * (20/21) = 8, 00, 00
31. The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
A. 20%
B. 18%
C. 15%
D. 12%
Answer and Explanation
option D
Using the formula: X + Y + XY/100
-20+10+(-200/100) = -10-2 = -12(- indicates decrease)
32. At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
A. 70%
B. 90%
C. 80%
D. 75%
Answer & Explanation
Answer: Option C
Explanation:
A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
33. If population of certain city increases at the rate of 5%. If population in 1981 was 138915, then population in 1978 was?
A. 1,20,000
B. 1,10,000
C. 1,00,000
D. 90,000
Answer & Explanation
Answer: Option A
Explanation:
X * (105/100) * (105/100) * (105/100) = 138915
X = 138915/1.157625
X = 120000
34. There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
A. 456
B. 744
C. 912
D. 1200
Answer & Explanation
Answer: Option B
Explanation:
W = 62% L = 38%
62% - 38% = 24%
24% -------- 288(1%= 288/24 =12)
62% -------- ? => 744(62*744)
35. Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
A. Nothing
B. 10%
C. 1%
D. 5%
Answer & Explanation
Answer: Option C
Using the formula: X + Y + XY/100
-10+10+((-10*10)/100)= 1%
36. A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
A. Rs.3600
B. Rs.4000
C. Rs.4500
D. Rs.3000
Answer & Explanation
Answer: Option A
Explanation:
X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
37. The population of a town is 45000; 5/9th of them are males and the rest females 40% of the males are married. What is the percentage of married females?
A. 60%
B. 50%
C. 45%
D. 40%
Answer & Explanation
Answer: Option B
Explanation:
Male = 45,000* 5/9 = 25,000
Female = 45,000* 4/9 = 20,000
Married Male = 25,000* 40/100 = 10,000
Married Female = 10,000
20,000 ------------ 10,000
100 ------------- ? => 50%
38. The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
A. 90% increase
B. 45% increase
C. 9% decrease
D. Same as before
Answer & Explanation
Answer: Option C
Using the formula: X + Y + XY/100
39. In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A. 173
B. 163
C. 153
D. 143
Answer & Explanation
Answer: Option C
Explanation:
44 + 28 + 10 = 82%
100 – 82 = 18%
850 * 18/100 = 153
40. When 5% is lost in grinding wheat, a country has to import 20 million bags; but when only 2% is lost, it has to import only 15 million bags. Find the quantity of wheat, which grows in the country?
A. 133 1/3 m
B. 150 m
C. 106 2/3 m
D. 166 2/3 m
Answer & Explanation
Answer: Option D
Explanation:
5% - 2% = 3%
3% ---- 5(20 million bag - 15 million bag)
100% ---- ? => 166 2/3
41. If P gets 25% more than Q, then by what percent does Q get less than P?
A. 33 1/3%
B. 30%
C. 20%
D. 16 2/3%
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
Let Q get 1 unit.
25% of 1 unit = 1/4 = 0.25
P gets (1 + 0.25) i.e., 1.25 units.
Difference = (1.25 - 1) = 0.25
Required percentage = 0.25/1.25 * 100 = 1/5 * 100 = 20%
42.At the special sale,5 tickets can be puchased for he price of 3 tickets.If 5 tickets are purchased at the sale, the amount saved will be what percent of
the orignal price of the 5 tickets?
A.20%
B.33 1/2%
C.40%
D.60%
Answer and Explanation
Answer: option C
Explanation:
let the initial price of each ticket be Rs.100
Then,orignal price of 5 tickets is Rs500
sale price of 5 tickets is Rs300
Amount saved=Rs(500-300)=200
Required percentage =((200/500)*100)=40%
43.solve[180% of (?)]/2=504
A.400
B.480
C.560
d.600
Answer and Explanation
option C
Explanation:
X*0.18=1008
X=1008*100/180=560
44.In a City, 35% of the population is composed of migrants, 20% of whom are from rural areas. Of the local population, 48% is female while this figure for rural and urban migrants is 30% and 40% respectively. If the total population of the city is 728400, what is its female population ?
A) 324138 B) 349680
C) 509940 D) None of these
Answer & ExplanationAnswer: A) 324138
Explanation:
Total Population = 728400
Migrants = 35 % of 728400 = 254940
local population = (728400 - 254940) = 473460.
Rural migrants = 20% of 254940 = 50988
Urban migrants = (254940 - 50988) = 203952
Female population = 48% of 473460 + 30% of 50988 + 40% of 203952 = 324138
45.n a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State ?
A) 4000 B) 8000
C) 12000 D) 16000
Answer & ExplanationAnswer: B) 8000
Explanation:
Let the number of candidates appeared from each state be x.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
46.A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets ?
A) 40% B) 45%
C) 50% D) 55%
Answer & ExplanationAnswer: C) 50%
Explanation:
Number of runs made by running = 120 - (3 x 4 + 8 x 6) = 120 - (60) = 60
Required percentage = [(60/120)*100] % = 50%
47.A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
A) 0.75D B) 0.76D
C) 0.765D D) None of the above
Answer & ExplanationAnswer: C) 0.765D
Explanation:
If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85D = 0.765D
48.Two numbers are 35% and 42% are less than a third number .How much percent is the second number less than the first ?
A) 10.769 % B) 11.23 %
C) 10.4 % D) 9.87 %
Answer & ExplanationAnswer: A) 10.769 %
Explanation:
I II III
65 58 100
65 -------- 7
100 ------ ? => 10.769%
49.Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
A) 0.15% B) 15%
C) 0.125% D) None of these
Answer & ExplanationAnswer: D) None of these
Explanation:
Total land of Sukhiya = 480x/0.6 = 800x
Cultivated land of village = 384000x
Required percentage = 800x/384000x 100 = 0.20833
50.A Shopkeeper charges sales tax of x% upto Rs.2,000 and above it he charges y%. A customer pays total tax of Rs 320, when he purchases the goods worth Rs. 6,000 and he pay's the total tax of Rs. 680 for the goods worth Rs. 12,000. The value of (x-y) is:
A) 0 B) -2
C) -4 D) 5
Answer & ExplanationAnswer: B) -2
Explanation:
2000xX/100 + 4000xY/100 = 320
and 2000xX/100 + 10000xY/100 = 680
x = 4 and y = 6
x-y = -2
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