Problems on profit and loss are the most favourite topic of GMAT Quant Section. If you have a clear concept of what is meant by cost price and selling price of a product, then with few formulas, you can master yourself in solving an ample number of questions. GMAT will not ask straightforward questions based on formulas directly, but we are discussing few questions with their detailed solution to aid you in clearing your basics.

**Profit & Loss Formulas**

Cost price (CP) is the price at which an article is purchased.

Selling price (SP) is the price at which an article is sold.

If SP > CP, it is a profit or gain

If CP > SP, it is a loss.

Gain or Profit = SP – CP

Loss = CP – SP

Loss or gain is always reckoned on CP

**Profit Percentage (Profit %)**

\(\frac{Profit}{CP} \times 100 = \frac{(SP – CP)}{CP} \times 100\)

**Loss Percentage (Loss %)**

\(\frac{Loss}{CP} \times 100 = \frac{(CP – SP)}{CP} \times 100\)

**In the case of a gain or profit, **

\(SP = \frac{(100 + Gain \%)}{100} \times CP\)

\(CP = \frac{100}{(100 + Gain \%)} \times SP\)

## Sample Questions on Profit & Loss

**1. If the selling price of 25 goods is equal to the cost price of 20 goods, what is the % loss or % profit made?**

Let the CP of 1 article be Rs.1.

Hence, CP of 20 goods = 20 * 1 = Rs. 20

SP of 25 goods = cost price of 20 goods = RS.20.

Let us find the CP of 25 goods.

Cost price of 25 goods = 25 * 1 = Rs. 25.

Therefore, profit made on sale of 25 goods = Selling price of 25 goods – cost price of 25 goods

= 20 – 25 = -Rs. 5.

Because the profit is the negative, it is a loss of Rs. 5.

Therefore, % loss = Loss /CP∗100

% loss = 5/25∗100 = 20% loss.

**2. Sam purchases 10 apples for Rs. 1. At what price should he sell a dozen apples if he wants to make total profit of 25%?**.

The CP of 1 apple = 1/10 or Rs.0.10.

As Sam wants to make a profit of 25%, his SP per apple should be 0.10 + 0.25* 0.10 = 0.1 + 0.025 = Rs. 0.125.

If the SP of 1 apple is Rs. 0.125, the SP of a dozen apples = 12 * 0.125 = Rs. 1.5

**3. What is the maximum percentage discount that a shopkeeper should offer on his quoted price so that he ends up selling at no profit or loss, if he had initially quoted his goods up by 50%?**

Let the CP of the goods to be Rs. 100.

He initially quoted his goods up by 50%.

Therefore, a 50% mark up would have resulted in him quoted price being Rs.100 + 50% of Rs. 100 = Rs. 100 + Rs. 50 = Rs. 150.

He sells the product at no profit or loss.

Therefore, he sells the product at CP, which is RS. 100.

Hence, he offers a discount of Rs. 50 on her marked price of Rs 150.

Hence, the % discount offered by her = (Discount/ Marked Price)∗100=(50/150)∗100= 33.33%

**4. A dealer who marked his commodity up by 50% subsequently offered a discount of 20% on the quoted price. What is the percentage profit the merchant made after offering the discount?**

The easiest way is to assume a value for the merchant’s cost price.

Therefore, it is best to assume the cost price to be Rs. 100.

The merchant marks his commodity up by 50%.

Therefore, his marked price (quoted price) = cost price + mark up.

Marked price = Rs. 100 + 50% of Rs. 100 = 100 + 50 = Rs. 150.

The merchant gives a discount of 20% on his quoted price.

Discount offered = 20% of 150 = Rs. 30.

Therefore, he sold his commodity for Rs. 150 – Rs. 30 = Rs. 120.

We assumed his cost to be Rs. 100 and he sold it finally for Rs.120.

Hence, his profit = Rs. 20 on his cost of Rs. 100.

Hence, his % profit = profit/CP * 100 = (20/100) * 100 = 20%.

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