Profit, loss and discount for IBPS PO

Profit and loss questions look like shop stories, but underneath they are percentage questions with three prices: what the seller paid, what they asked for, and what they got. Once you know which price each percentage is measured on, the story falls away and you are left with a line of multiplication.

In IBPS PO, the topic turns up as standalone arithmetic in the prelims, inside quantity comparison and data sufficiency, and in mains DI, where a table of cost and selling prices asks for profit percentages. It rewards the multiplier method more than any formula list.

The three prices and their bases

• Profit % = (SP − CP) ÷ CP × 100. Loss % uses CP − SP.
• Discount % = (MP − SP) ÷ MP × 100.
• Mark-up % is how far MP is above CP, measured on CP.

The multiplier method

Turn every percentage into a factor and chain them.

• CP to MP with a mark-up of m%: × (1 + m/100).
• MP to SP with a discount of d%: × (1 − d/100).
• So SP = CP × (1 + m/100) × (1 − d/100).

Why it works: each step is a percentage change on the previous price, and a percentage change is a multiplication. Chaining the factors gives SP as a multiple of CP, and that multiple minus 1 is the profit or loss as a fraction.

Successive discounts also multiply. Discounts of 20% and 10% give 0.8 × 0.9 = 0.72, a total discount of 28%, not 30%.

Four patterns worth knowing

1. "SP of x articles = CP of y articles." Take each article's CP as ₹1. Then x articles sell for ₹y and cost ₹x. Profit % = (y − x) ÷ x × 100. If y is less than x, it is a loss.

2. Same SP, one at x% profit and one at x% loss. There is always a net loss of x²/100 per cent. Why: the loss-making item had the higher cost price, so the loss is on the bigger base.

3. False weights. A seller who claims to sell at cost price but gives g grams instead of 1,000 makes a profit of (1,000 − g) ÷ g × 100. Why: they receive the price of 1,000 grams while paying for only g grams.

4. Buy x, get y free. The buyer pays for x items but takes x + y. Effective discount = y ÷ (x + y) × 100.

Eight worked examples

Example 1: A shopkeeper marks goods 40% above cost and gives a 25% discount. Find the profit or loss.

• 1.4 × 0.75 = 1.05. A 5% profit.

Example 2: The SP of 20 articles equals the CP of 25 articles. Find the profit %.

• Twenty articles sell for ₹25 and cost ₹20.
• Profit = 5 ÷ 20 × 100 = 25%.

Example 3: Two items are each sold for ₹1,200, one at 20% profit and the other at 20% loss. Find the overall result.

• CPs: 1,200 ÷ 1.2 = 1,000 and 1,200 ÷ 0.8 = 1,500. Total CP = 2,500. Total SP = 2,400.
• Loss = 100 ÷ 2,500 × 100 = 4%.
• Shortcut: 20²/100 = 4% loss.

Example 4: A shopkeeper gives a 10% discount and still makes a 17% profit. The CP is ₹500. Find the MP.

• SP = 500 × 1.17 = 585.
• MP = 585 ÷ 0.9 = ₹650.

Example 5: A dealer claims to sell rice at cost price but uses a 900 g weight for 1 kg. Find the profit %.

• Profit = 100 ÷ 900 × 100 = 11 1/9%, about 11.11%.
• The base is 900, what the dealer actually gave, not 1,000.

Example 6: A shop offers "buy 4, get 1 free". What is the effective discount?

• The buyer pays for 4 and takes 5.
• Discount = 1 ÷ 5 × 100 = 20%.

Example 7: By what percentage above cost must a seller mark goods to gain 20% after giving a 20% discount?

• MP × 0.8 = CP × 1.2, so MP = 1.5 × CP.
• Mark-up = 50%.

Example 8: A trader sells an item at a 10% loss. Had it been sold for ₹90 more, there would have been a 5% profit. Find the CP.

• The swing from −10% to +5% is 15% of CP.
• 15% of CP = 90, so CP = ₹600.

Common mistakes

• Taking discount on CP instead of MP.
• Adding successive discounts. Multiply the factors.
• Assuming equal costs in "same selling price" questions. The costs differ, which is why there is a net loss.
• Using 1,000 as the base in false-weight questions.
• Counting free items as a discount on the free item only. The discount is spread over everything the buyer takes.

Practice set

1. CP = ₹800. The item is marked 50% above cost and sold at a 20% discount. Find the SP and the profit %.
2. The SP of 15 articles equals the CP of 18. Find the profit %.
3. After a 15% discount, an item sells for ₹1,700. Find the MP.
4. Find the single discount equal to successive discounts of 25% and 20%.
5. A trader gains 10% by selling an item for ₹660. Find the CP.
6. A trader marks goods 25% above cost and gives a 12% discount. Find the profit %.
7. What is the effective discount in a "buy 3, get 1 free" offer?
8. A dealer uses an 800 g weight for 1 kg and also sells at 10% above cost price. Find the actual profit %.

Answers:

1. ₹960; 20% profit. 800 × 1.5 × 0.8 = 960.
2. 20%. Fifteen articles sell for ₹18 and cost ₹15; 3 ÷ 15 × 100.
3. ₹2,000. 1,700 ÷ 0.85.
4. 40%. 0.75 × 0.8 = 0.6.
5. ₹600. 660 ÷ 1.1.
6. 10%. 1.25 × 0.88 = 1.10.
7. 25%. Pay for 3, take 4; 1 ÷ 4 × 100.
8. 37.5%. The dealer receives 1.1 × (price of 1,000 g) for 800 g. 1,100 ÷ 800 = 1.375.

What to do next

• Solve ten mixed questions a day for a week using only the multiplier method.
• Revise the base rules in the percentage guide; every profit question depends on them.
• Practise profit-based comparisons in quantity comparison sets.
• Move on to simple and compound interest, which uses the same factor idea over time.