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1. A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share? |
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A. |
Rs. 500 |
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B. |
Rs. 1500 |
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C. |
Rs. 2000 |
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D. |
None |
Solution:
Option(C) is correct
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x
respectively.
Then, 4x−3x=1000
⇒x=1000
B's share =Rs.2x=Rs.(2×1000)= Rs. 2000
2.
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A and B together have Rs. 1210. If 415 of A's amount is equal to 25 of B's amount, how much amount does B have? |
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A. |
Rs 460 |
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B. |
Rs 484 |
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C. |
Rs 550 |
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D. |
Rs 664 |
Solution:
Option(B) is correct
Given
4/15×A =2/5×B
⇒A=3/2×B
A/B=3/2
BB's share = Rs.1210×2/5= Rs. 484
3. The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
· A. 36
· B. 24
· C. 12
· D. 6
Answer & Explanation
Answer: Option C
Explanation:
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
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4. In a mixture 60 litres, the ratio of milk and water 2:1. If the this ratio is to be 1:2, then the quantity of water 1to be further added is: |
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A. |
20 litres |
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B. |
30 litres |
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C. |
40 litres |
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D. |
60 litres |
Solution:
Option(D) is correct
Quantity of milk = 60×2/3=40 litres
Quantity of water in it =(60−40) litres =20 litres.
New ratio =1:2
Let, the quantity of water to be added further be x litres.
Then milk : water = 40/20+
Now,
40/20+x=1/2
20+x=80
X=60.
5.
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Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: |
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A. |
2:5 |
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B. |
3:5 |
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C. |
4:5 |
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D. |
5:4 |
Solution:
Option(C) is correct
Let the third number be x.
Then, first number = 120% of x= 120x/100=6x/5
Second number = 150% of x = 150x/100=3x/2
Ratio of first two numbers = 6x/5:3x/2=4:5
6.
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A sum of Rs. 36.90 is made up of 180 coins which are either 10 paise coins or 25 p coins. The number of 10 p coins is: |
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A. |
48 |
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B. |
54 |
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C. |
56 |
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D. |
60 |
Solution:
Option(B) is correct
Step (i) Total number of coins = 180
Let xx be number of 10p coins and y be number of 25p coins
x+y=180 --------(i)
Step (ii) Given 10p coins and 25p coins make the sum = Rs. 36.90
10x/100+25y/100⇒10x+25y=36.9=3690-----(ii)
Step (iii)
Solving (i) and (ii),
10x+10y10x+25y−15yy=1800=3690=1890=126
Substitute y value in equation (i)
x=180–126=54
Number of 10p coins = 54
7. 1: 3 = 1 2/3: x. The value of x is?
· A. 1
· B. 3
· C. 4 1/6
· D. 5
Answer & Explanation
Answer: Option D
Explanation:
x * 1 = 3 * 5/3
x = 5
8. What number has a 5:1 ratio to the number 10?
· A. 42
· B. 50
· C. 55
· D. 62
Answer & Explanation
Answer: Option B
Explanation:
5:1 = x: 10
x = 50
9. If a: b = 7: 5, b: c = 9: 11, find a: b: c?
· A. 63: 14: 55
· B. 63: 45: 55
· C. 14: 14: 15
· D. 7: 14: 15
Answer & Explanation
Answer: Option B
Explanation:
a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
10. If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?
· A. 5:12
· B. 7:12
· C. 3:11
· D. 5:11
Answer & Explanation
Answer: Option A
Explanation:
a/d = (3/4)*(7/9)*(5/7) => 5/12
11. Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
· A. Rs.600
· B. Rs.525
· C. Rs.375
· D. Rs.0
Answer & Explanation
Answer: Option C
Explanation:
A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
12. Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
· A. Rs.260
· B. Rs.270
· C. Rs.360
· D. Rs.540
Answer & Explanation
Answer: Option D
Explanation:
A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
13. A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
· A. Rs.50
· B. Rs.75
· C. Rs.100
· D. Rs.150
Answer & Explanation
Answer: Option A
Explanation:
A+B+C = 500
A+C = 200
B+C = 350
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A+B+2C = 550
A+B+C = 500
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C = 50
14. In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
· A. 32
· B. 42
· C. 52
· D. 60
Answer & Explanation
Answer: Option B
Explanation:
5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
15. The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.950 find the number of laborers?
· A. 18
· B. 20
· C. 22
· D. 24
Answer & Explanation
Answer: Option D
Explanation:
1 ------ 6
4 ------? è 24
16. x varies inversely as square of y. Given that y = 2 for x = 1. The value of x for y = 6 will be equal to:
· A. 3
· B. 9
· C. 1/3
· D. 1/9
Answer & Explanation
Answer: Option D
Explanation:
Given x = k/y2, where k is a constant.
Now, y = 2 and x = 1 gives k = 4.
x = 4/y2 => x = 4/62, when
y = 6 => x = 4/36 = 1/9.
17. If 10% of x = 20% of y, then x:y is equal to:
· A. 1:2
· B. 2:1
· C. 5:1
· D. 10:1
Answer & Explanation
Answer: Option B
Explanation:
10% of x = 20% of y
10x/100 = 20y/100 => x/10 = y/5
x/y = 10/5 = 2/1
x:y = 2:1.
18. The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
· A. 3:3:10
· B. 10:11:20
· C. 23:33:60
· D. Cannot be determined
Answer & Explanation
Answer: Option C
Explanation:
Let A = 2k, B = 3k and C = 5k
A's new salary = 115/100 of 2k = 23/10 k
B's new salary = 110/100 of 3k = 33/10 k
C's new salary = 120/100 of 5k = 6k
New ratio = 23k/10 : 33k/10 : 6k = 23:33:60
19. If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is:
· A. Rs. 182
· B. Rs. 190
· C. Rs. 196
· D. Rs. 204
Answer & Explanation
Answer: Option D
Explanation:
Given ratio = 1/2:2/3:3/4 = 6:8:9
1st part = 782 * 6/23 = Rs. 204.
20. Two numbers are in the ratio 1:2. If 7 is added to both, their ratio changes to 3:5. The greatest number is:
· A. 24
· B. 26
· C. 28
· D. 32
Answer & Explanation
Answer: Option C
Explanation:
Let the numbers be x and 2x.
Then, (x + 7)/(2x + 7) = 3/5
x = 14
Greatest number = 2 * 14 = 28.
21. 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
· A. 30
· B. 60
· C. 45
· D. 90
· E. None of these
Answer & Explanation
Answer: Option B
Explanation:
Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
22. If A:B:C = 2:3:4, then A/B : B/C : C/A is equal to:
· A. 4:9:16
· B. 8:9:12
· C. 8:9:16
· D. 8:9:24
Answer & Explanation
Answer: Option D
Explanation:
Let A = 2x, B = 3x and C = 4x.
Then, A/B = 2x/3x = 2/3, B/C = 3x/4x = 3/4 and C/A = 4x/2x = 2/1
A/B : B/C : C/A = 2/3 : 3/4 : 2/1 = 8:9:24
23. If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then A:B:C:D is:
· A. 16:22:30:35
· B. 16:24:15:35
· C. 16:24:30:35
· D. 18:24:30:35
Answer & Explanation
Answer: Option C
Explanation:
A:B = 2:3, B:C = 4:5 = (4 * 3/4):(5 * 3/4) = 3:15/4
and C:D = 6:7 = (6 * 15/24):(7 * 15/24) = 15/4:35/8 A:B:C:D = 2:3:15/4:35/8 = 16:24:30:35
24. If x;Y = 5:2, then (8x + 9y):(8x + 2y) is :
· A. 22:29
· B. 26:61
· C. 29:22
· D. 61:26
Answer & Explanation
Answer: Option C
Explanation:
Let x = 5k and y = 2k.
Then, (8x + 9y)/(8x + 2y)
= [(8 * 5k) + (9 * 2k)] / [(8 * 5k) + (2 * 2k)] = 58k/44k = 29/22
(8x + 9y):(8x + 2y) = 29:22
25. Find the mean proportional of the following pairs of numbers 6 and 24.
· A. 8
· B. 12
· C. 16
· D. 18
· E. None of these
Answer & Explanation
Answer: Option B
Explanation:
26. Find the mean proportional of the following pairs of numbers 50 and 512.
· A. 80
· B. 120
· C. 160
· D. 200
· E. None of these
Answer & Explanation
Answer: Option C
Explanation:
27. In an exam, a candidate secured 504 marks our of the maximum mark of M. If the maximum mark M is converted into 800 marks, he would have secured 384 marks. What is the value of M?
· A. 750
· B. 1200
· C. 1125
· D. 975
· E. None of these
Answer & Explanation
Answer: Option E
Explanation:
504/M = 384/800
(504 * 800) / 384 = M
M = 1050
28. In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.
· A. 420
· B. 528
· C. 494
· D. 464
· E. None of these
Answer & Explanation
Answer: Option B
Explanation:
Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
29. The ratio of the incomes of Chetan and Dinesh is 3 : 4. The ratio of their expenditures is 5 : 7. If each of them saves Rs. 200, find the incomes of both ?
· A. Rs. 1500, Rs. 2000
· B. Rs. 600, Rs. 800
· C. Rs. 900, Rs. 1200
· D. Rs. 1800, Rs.2400
· E. None of these.
Answer & Explanation
Answer: Option E
Explanation:
Let the incomes of Chetan and Dinesh be 3x and 4x respectively. Let the expenditures of Chetan and Dinesh be 5y and 7y respectively. Savings is defined as (Income) - (Expenditure). Hence the savings of Chetan and Dinesh are 3x - 5y and 4x - 7y respectively.
3x - 5y = 200 --> (1)
4x - 7y = 200 --> (2)
Multiplying (1) by 7 and (2) by 5 and subtracting the resultant equation (2) from resultant equation (1), we get, x = 400
The incomes of Chetan and Dinesh are 3x = Rs.1200 and 4x = Rs.1600 respectively.
30. In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
· A. 1 : 2
· B. 3 : 4
· C. 1 : 4
· D. 2 : 3
· E. None of these
Answer & Explanation
Answer: Option E
Explanation:
Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1 : 3.
31.
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A and B
together have Rs. 1210. If |
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Answer: Option B Explanation:
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32.
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Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is: |
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Answer: Option C Explanation: Let the third number be x.
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33.
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Answer: Option C Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then, 4x - 3x = 1000
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34.
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Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats? |
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Answer: Option A Explanation: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
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35.
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Answer: Option D Explanation:
Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x litres.
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36.
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Answer: Option C Explanation: Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x).
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37.
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Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary? |
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Answer: Option D Explanation: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000. |
38.
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Answer: Option B Explanation:
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39.
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Answer: Option B Explanation: Let the three parts be A, B, C. Then,
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40.
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Answer: Option D Explanation: Given ratio
=
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41.
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The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries? |
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Answer: Option C Explanation: Let A = 2k, B = 3k and C = 5k.
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42.
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Answer: Option C Explanation:
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43.
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The fourth proportional to 5, 8, 15 is: |
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Answer: Option B Explanation: Let the fourth proportional to 5, 8, 15 be x. Then, 5 : 8 : 15 : x
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44.
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Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is: |
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Answer: Option B Explanation: Let the numbers be 3x and 5x.
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45.
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Answer: Option C Explanation: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Hence, the number of 5 p coins = (3 x 50) = 150. |
46. The ratio of A’s salary to B’s was 4 : 5. A’s salary is increased by 10% and B’s by 20%, what is the ratio of their salaries now?
A. 14:11
B. 15:14
C. 11:15
D. None of these
Answer & Explanation
Option C
Present ratio = 4 : 5. Increase of 10% and 20%. \New ratio of salaries will be 4 × 1.1
:5 × 1.2 = 11 : 15.
47. The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond of the same kind weighing 8 decigrams.
A. Rs. 762
B. Rs. 760
C. Rs. 764
D. Rs. 768
Answer & Explanation
Option D
C α W2 ⇒ C = kW2. 4800 = k(20)2 ⇒ k = 12. Now C = 12(8)2 ⇒ C =768.
48. The ratio of two numbers is 9 : 5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.
A. 72, 40
B. 18, 10
C. 36, 20
D. None of these
Answer & Explanation
Option C
Present ratio = 9 : 5. ∴actual
values are 9x and 5x.
Hence 9x + 9 : 5x – 5 = 3 : 1 ⇒ x = 4. ∴ numbers are 9(4) = 36 and 5(4) = 20.
49. Find the ratio of the diagonal of a square of side 30 cm, to its side.
A. √2: 3
B. √3: 4
C. 1 : √2
D. √2: 1
Answer & Explanation
Option D
Diagonal of a square = √2 side. Hence this is the required ratio. So the
required ratio is √2: 1.
50. The ratio of the first and second-class fares between the two stations is 6 : 4 and the number of passengers traveling by first and second-class is 1 : 30. If Rs. 2100 is collected as fare, what is the amount collected from first class passengers?
A. Rs.250
B. Rs. 200
C. Rs. 150
D. Rs. 100
Answer & Explanation
Option D
Ratio of the amounts collected from 1st and 2nd class = (6 × 1): (4 × 30) = 1 : 20. ∴ Amount collected from 1st class passengers =1/21 × 2100 = 100
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