PROFIT AND LOSS

                                      PROFIT AND LOSS

 

A profit and loss statement or P&L is an account compiled to show gross and net profit or loss, during a specific time period. Profit or loss is equal to your income minus your expenses.

Profit and loss statements show you how much money you’re making or losing in a specific time period, they allow you to compare past performance, and detect any issues with sales margins and expenses.

 

Basic Definitions and Formulas:

·        Cost price (C.P.): This is the price at which an article is purchased.

·        Selling price (S.P.): This is the price at which an article is sold.

·        Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit incurred.

Formula: Profit or Gain = S.P. – C.P.

·        Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.

                                        Formula: Loss = Cost price (C.P.) – Selling Price (S.P.)

 

·        Profit or Loss is always calculated on the cost price.

·        Marked price: This is the price marked as the selling price on an article, also known as the listed price.

·        Discount or Rebate: This is the reduction in price offered on the marked or listed

price.

                       Formula: Discount = Marked price(M.P.) -  Selling Price (S.P.)

 

·        Markup: It is the MRP given in the shop.

                                           Formula: Markup = Marked price(M.P.) – Cost price (C.P.)

          

        Below is the list of some basic formulas used in solving questions on profit and loss:

·        Gain % = (Gain / CP) * 100

·        Loss % = (Loss / CP) * 100

·        SP = [(100 + Gain%) / 100] * CP

·        SP = [(100 – Loss %) / 100]*CP

The above two formulas can be stated as,

If an article is sold at a gain of 10%, then SP = 110% of CP.

If an article is sold at a loss of 10%, then SP = 90% of CP.

·        CP = [100 / (100 + Gain%)] * SP

·        CP = [100 / (100 – Loss%)] * SP

·        CP (1+m%) = MP

·        MP (1-d%)  = SP

·        CP (1+p%)  = SP

 

Successive Discount:

If discount is given in rupees then , d = d1 + d2

If discount is given in percentages then ,

 (1 - D%) = (1 – d1%) (1 – d2%)     or      D% = d1 + d2 + d1 d2/100

 

Successive Profit:

Formula for successive profit is  a + b + a b/100

 

Weighted Average Profit:

Average  in terms of marks =  Total marks/ Total population

 

Example 1: 

A cloth merchant bought 35 shirts, each at a price of Rs 280. He sold each of them for Rs. 308. Find his percentage profit.

Sol: The profit percentage remains same for one unit as well for all the units. Thus the calculations should be done for one unit only.
CP = Rs. 280. SP = Rs. 308.
Profit = 308 – 280 = Rs. 28. Now you need to apply profit percentage formula for the same.
Profit percentage = 100 × 28/280 = 10%

 

Example 2:

 An article is sold for Rs 2400 at a profit of 25 %. What would have been the actual profit or loss if it had been sold at Rs 1800?

Sol: Firstly let us find the cost price of the same. C.P. = 2400 × 100/125 = 1920.
New selling price = Rs. 1800 ⇒ Loss = 1920 – 1800 = 120
∴ Loss percentage = 100 × 120/1920 = 6.25%.

 

Example 3:

 A retail fruit vendor buys pineapples at a score for Rs 200, and retails them at a dozen for Rs 156. Did he gain or lose in the transaction and what % was his gain or loss?

Sol: C.P = Rs. 220/score ∴ C.P/Pineapple = 200/20 = 10 (Note: 1 score = 20 nos.)
S.P = Rs.156/dozen ∴ S.P/Pineapple = 156/12 = 13. Profit = Rs. 3.
∴ % Profit = 100 × 3/10 = 30%

 

Example 4: 

If an article is sold at a loss of 66 2/3%, what is the loss in terms of the selling price?

Sol: Let the C. P. = 100. ∴ Amount of loss = 66 2/3 or 200/3 ⇒ S. P = 100 – 66 2/3 = 33 1/3 or 100/3.
∴ Loss expressed in terms of S. P. = 100 × (200/3)/(100/3) 100 = 200 %

 

 

Example 5:

 Profit obtained by selling a floppy disc at Rs. 320 is equal to 7/5th of the profit obtained by selling the same floppy disc at Rs. 300. What is the cost price of the watch?

Sol: Let the cost of a watch be x ∴ (320 - x) = 7/5 × (300 - x).
So 1600 – 5x = 2100 – 7x. ⇒ 2x = 500 ⇒ x = Rs. 250.

 

Example 6:

 A man sells two chairs for Rs. 480 each. On one he makes a profit of 20 % and on the other he makes a loss of 20 %. Find his total loss/gain in these two transactions (in Rs.).

Sol: Here the amount of loss can be directly found by the formula given in the formula section of this article.
The amount of loss = 2.p².S.P/100²-p² ∴ ⇒ Loss = 2.20².480/100²-20² = 40. So net loss = Rs. 40.

 

Example 7: 

Mukesh purchased two watches at the same price and sold one at a profit of 20 % and the other at a profit of 22.5%. If the difference between the two selling price is Rs 150, what is the cost price of each of the watches?

Sol: Let the cost price of the watches = 100. The selling price of the first watch = 120 and the selling price of the second watch = 122.5.
The difference in the selling price = 2.5 if the cost price = 100
If the difference in selling price = 150, then the cost price = 150 × 100/2.5 = Rs. 6000.

 

 

Example 8:

 A merchant buys 30 kg of rice at Rs 40/kg, and another 20 kg of rice at Rs 30/kg. He mixes them and sells half of the mixture at Rs. 36/kg. At what price should he sell the remaining mixture to get an overall profit of 30%?

Sol: Total cost for the entire quantity of rice = (30 × 40) + (20 × 30) = Rs. 1800.
If his profit is 30%, then the sales realization = 1.3 1800 = Rs. 2340.
He sells 25 kg at Rs. 36/kg = Rs. 900. Therefore to make the said amount of profit, he should sell the remaining 25 kg of rice at Rs. 2340 – Rs. 900 = Rs.1440
∴ The selling price of a kg of rice for the remaining 25 kg = 1440/25 = Rs. 57.6.

 

Example 9: 

What should each of the forty shirts be sold at, the cost of each of which is Rs. 500, so as to get a profit equal to the selling price of 20 of them?

Sol: S.P. of 20 Shirts = S.P of 40 Shirts – C.P. of 40 Shirts
20 S.P. = 40 S.P – 40 × 500 ⇒ 20 S.P = 20000 ⇒ S.P = Rs. 1000.

 

Example 10: 

Three - eighth of 320 chairs was sold at a profit of Rs. 50 each and the rest for Rs. 33600. If the seller makes a profit of 20 % on the whole transaction, what is the cost price of each of the chair?

Sol: 120 chairs were sold at a profit of Rs. 50 each. Profit on these 120 chairs = 6000.
S. P. of all 320 chairs = C. P. of 120 chairs + Profit on 120 chairs + S. P. of 200 chairs
= (120 × C.P) + 6000 + 33600 = (120 × C. P.) + 39600
But these 320 chairs were sold at a profit of 20 %. S. P. = 1.2 × C.P
⇒ 320 × 1.2 × C.P = 120 × C. P. + 39600 ⇒ 384 C.P = 120 C.P + 39600 ⇒ C. P. = 150.

 

 

Example 11: 

A package tour operator allows a 25 % discount on his advertised price and then makes a profit of 20 %. What is the advertised price on which he gains Rs. 60?

Sol: Profit = Selling price – Cost Price = 60. Selling price = 1.2 (C. P.) ⇒ 1.2 C.P – C. P. = 60.
⇒ 0.2 C. P. = 60 ⇒ C. P. = 300 and Selling price = 360.
List price or advertised price ⇒ (0.75) = Selling price ⇒ List price = Selling price/0.75 = 360/0.75 = Rs. 480.

 

 

Example 12

A manufacturer estimates that on inspection 20% of the articles he produces are rejected. He accepts an order to supply 20,000 articles at Rs. 7.50 per item. He estimates the profit on his outlay to be 20 % after providing for the rejects. Find his cost of manufacture per article.

Sol: S.P = Rs. 7.5 per item × For 20,000 items = 150,000
Minimum no. of items that need to be produced so that after providing for 20 % rejection he still has 20,000 items = 20000/0.8 = 25,000.
As he makes a profit of 20%, then his cost price will be = 150000/1.2 = Rs. 125000.
Now he is producing 25000 units at a cost of 125000, thus the CP per item = 125000/25000 = Rs. 5.

 

Example 13: 

A man sold Pentium computers at a profit of 6 %. Had he made a loss of 5 % instead due to a price crash, he would have sold it for Rs 3,850 less. What was his cost price and selling price in each of the instances?

Sol: C. P. (1.06) = S.P.₁
C. P. (0.95) = S.P.₂
S. P.₁ - S. P.₂ = 3850 ⇒ C. P. (1.06 – 0.95) = 3850 ⇒ 0.11 C. P. = 3850 ⇒ C. P. = 35,000.
And S. P.₁ = 1.06 × 35,000 = 37,100 and S. P.₂ = 0.95 × 35,000 = 33,250

Example 14: 

Trader A offers a discount of 25 % on the marked price for cash purchase. Trader B offers a trade discount of 20 % and a cash discount of 5 % on the same article marked at the same price as that of Trader A. As a buyer whom should I buy from if I am to pay cash?

Sol: Trader A: If the marked price = 100 then the net price to the buyer = 0.75 × 100 = 75.
Trader B: If the marked price = 100, then the net price
= 0.8 × 100 = 80 and the cash price = 0.95 × 80 = 0.76.
Since the discount is higher or the price to me as a buyer is lower with Trader A, I should choose to buy from Trader A.