Use the following solved examples to understand the fundamentals of profit and loss:

**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.p^{2}.S.P/100^{2}-p^{2} ∴ ⇒ Loss = 2.20^{2}.480/100^{2}-20^{2} = 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.

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**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.