Profit, Loss and Discount: Formulas and Worked Examples

Profit, loss and discount questions test how well you can use percentages in everyday buying and selling. Lok Sewa papers ask them in simple forms (find the profit percent) and in trickier forms (find the cost price, combine discount and VAT). This note gives each formula with a worked example in rupees so you can see exactly how the steps go.

1. Basic terms

Remember: profit and loss are always worked out on the cost price, while discount is always worked out on the marked price.

• Example: A shopkeeper buys a used bicycle for Rs 4,500 and spends Rs 500 on repairs. His cost price is Rs 5,000. If he sells it for Rs 5,600, his profit is Rs 600.

2. Profit and loss percent

• Profit percent = profit / CP × 100
• Loss percent = loss / CP × 100

Worked examples:

• CP = Rs 1,200, SP = Rs 1,500. Profit = Rs 300. Profit percent = 300/1,200 × 100 = 25%.
• CP = Rs 2,000, SP = Rs 1,700. Loss = Rs 300. Loss percent = 300/2,000 × 100 = 15%.

Same number of articles trick: if the cost price of x articles equals the selling price of y articles, then profit percent = (x − y)/y × 100 (when x is more than y). For example, if the CP of 12 pens equals the SP of 10 pens, profit = (12 − 10)/10 × 100 = 20%.

3. Finding SP or CP from a percent

These formulas use the multiplying factor idea from percentages.

Worked examples:

• CP = Rs 800, profit 15%. SP = 800 × 115/100 = Rs 920.
• CP = Rs 2,400, loss 5%. SP = 2,400 × 95/100 = Rs 2,280.
• SP = Rs 1,320 with a profit of 10%. CP = 1,320 × 100/110 = Rs 1,200.
• SP = Rs 1,140 with a loss of 5%. CP = 1,140 × 100/95 = Rs 1,200.

Common trap: a 10% profit on SP is not the same as a 10% profit on CP. Unless the question clearly says otherwise, always take the profit percent on CP.

4. Marked price and discount

Shops usually mark a price higher than the cost price and then give a discount.

• Discount = MP − SP
• Discount percent = discount / MP × 100
• SP after a discount of d% = MP × (100 − d)/100
• MP needed for a given SP = SP × 100/(100 − d)

Worked examples:

• MP = Rs 2,500, discount 12%. Discount = 300, so SP = Rs 2,200.
• A watch marked Rs 1,600 is sold for Rs 1,360. Discount = 240, so discount percent = 240/1,600 × 100 = 15%.
• A trader wants to sell at Rs 1,800 after giving 10% discount. MP = 1,800 × 100/90 = Rs 2,000.

Marking above cost: if a trader marks goods m% above CP and then gives d% discount, the overall effect is m − d − (m × d)/100 percent (profit if positive, loss if negative).

• Example: Marked 40% above CP and sold at 20% discount. Effect = 40 − 20 − 8 = 12% profit. Check with CP = Rs 1,000: MP = 1,400; SP = 1,400 × 0.8 = 1,120; profit = 12%.

5. Successive discounts

Sometimes two discounts are given one after the other, for example “20% plus 10% off”. The second discount is on the reduced price, so the two cannot simply be added.

Single equivalent discount = a + b − (a × b)/100.

• Example: Discounts of 20% and 10% on MP Rs 5,000. Single equivalent = 20 + 10 − 2 = 28%. Check: 5,000 becomes 4,000 and then 3,600, which is 28% less than 5,000.
• Example: Discounts of 10% and 10% equal a single discount of 19%, not 20%.

6. Two articles at the same selling price

If two articles are sold at the same SP, one at r% profit and the other at r% loss, the trader always makes an overall loss of r²/100 percent.

• Example: Two radios are sold for Rs 990 each, one at 10% profit and one at 10% loss. CPs are 990 × 100/110 = Rs 900 and 990 × 100/90 = Rs 1,100. Total CP = Rs 2,000, total SP = Rs 1,980. Loss = Rs 20, which is 1% (10²/100 = 1).

7. VAT basics

Value Added Tax (VAT) is a tax added to the price of goods and services. In a bill, VAT is normally added after any discount.

• Amount with VAT = price × (100 + VAT rate)/100
• Price before VAT = amount with VAT × 100/(100 + VAT rate)

The examples below use a rate of 13 percent. Nepal’s standard VAT rate is 13 percent, but always use the rate given in the question.

• Example: At 13 percent VAT, an item priced Rs 2,000 has VAT of Rs 260, so the customer pays Rs 2,260.
• Example (reverse): A bill of Rs 3,390 includes 13 percent VAT. Price before VAT = 3,390 × 100/113 = Rs 3,000, and VAT = Rs 390.
• Example (discount then VAT): MP = Rs 4,000, discount 10%, then 13 percent VAT. Price after discount = Rs 3,600. VAT = 3,600 × 13/100 = Rs 468. Amount paid = Rs 4,068.

8. Step-by-step method for any question

• Write down what is given: CP, SP, MP, profit or loss percent, discount, VAT rate.
• Decide the base: CP for profit and loss, MP for discount, the price after discount for VAT.
• Convert each percent into a multiplying factor, such as 1.15 for a 15% profit or 0.9 for a 10% discount.
• Multiply the factors in the order the events happen.
• Check that the answer is sensible: SP should be more than CP when there is a profit.