Profit, Loss & Discount

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Quick recall

• Profit and loss percentages use cost price; discount uses marked price.
• CP = cost price, SP = selling price, MP = marked price.

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Formula Cards

1. Profit and loss

$$\text{Profit}=SP-CP,\qquad\text{Loss}=CP-SP$$

2. Profit percentage

$$\text{Profit (\%)}=\frac{SP-CP}{CP}\times100$$

3. Loss percentage

$$\text{Loss (\%)}=\frac{CP-SP}{CP}\times100$$

4. Selling price from cost

$$SP=CP\left(1+\frac{p}{100}\right)$$

For loss of l%, use the factor (1 − l/100).

5. Discount percentage

$$\text{Discount (\%)}=\frac{MP-SP}{MP}\times100$$

6. Selling price after discount

$$SP=MP\left(1-\frac{d}{100}\right)$$

7. Equal selling prices; equal gain and loss rates

$$\text{Overall loss (\%)}=\frac{x^2}{100}$$

Two articles sell at the same SP, one at x% profit and the other at x% loss. Assume 0 < x < 100.

Worked Examples

Example 1

Question: CP = Rs. 200; SP = Rs. 250. Find profit percentage.

Step 1: Find the profit.

$$250-200=50$$

Step 2: Divide by cost price.

$$\frac{50}{200}\times100=25\%$$

Answer: 25% profit.

Example 2

Question: MP = Rs. 1,000; discount = 15%. Find SP.

Step 1: Find the price factor.

$$1-0.15=0.85$$

Step 2: Multiply by marked price.

$$SP=1000\times0.85=850$$

Answer: Rs. 850.

Example 3

Question: An item sells for Rs. 600 at 20% profit. Find CP.

Step 1: Express SP in terms of CP.

$$600=1.20\,CP$$

Step 2: Divide by the profit factor.

$$CP=\frac{600}{1.20}=500$$

Answer: Rs. 500.

Example 4

Question: Goods are marked 40% above cost, then discounted by 10%. Find net profit percentage.

Step 1: Assume a cost price of 100.

$$MP=100\times1.40=140$$

Step 2: Apply the discount.

$$SP=140\times0.90=126$$

Step 3: Compare selling price with cost.

$$\frac{126-100}{100}\times100=26\%$$

Answer: 26% profit.

Example 5

Question: Two items sell for Rs. 990 each, one at 10% profit and the other at 10% loss. Find overall loss percentage.

Step 1: Recover the two cost prices.

$$CP_1=\frac{990}{1.10}=900,\qquad CP_2=\frac{990}{0.90}=1100$$

Step 2: Find totals and loss.

$$CP=2000,\qquad SP=1980,\qquad\text{Loss}=20$$

Step 3: Calculate the loss percentage.

$$\frac{20}{2000}\times100=1\%$$

Answer: 1% overall loss.

Drill

Try each question before opening its answer.

Question 1

CP=400, SP=460. Find profit%.

• Show answer

  15%

Question 2

CP=800, loss=10%. Find SP.

• Show answer

  720

Question 3

MP=1200, SP=1000. Find discount%.

• Show answer

  16.67%

Question 4

An article sold at 25% profit for Rs.500. Find CP.

• Show answer

  400

Question 5

A trader marks up 50% then gives 20% discount. Net profit%?

• Show answer

  20%

Question 6

If CP=SP, what is profit%?

• Show answer

  0%

Question 7

An item bought for 300, sold for 270. Loss%?

• Show answer

  10%

Question 8

To gain 20% after a 10% discount on MP, MP must be what % above CP?

• Show answer

  33.33%

Question 9

A dealer offers 2 successive discounts of 10% and 5% on MP 1000. Find SP.

• Show answer

  855

Question 10

Find CP if SP=690 after a 15% loss.

• Show answer

  Rs. 811.76 (approximately)

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