Profit, loss and discount for IBPS Clerk

Profit and loss is percentage with a shop attached. Clerk papers usually carry an arithmetic word problem or two from this family, and it also turns up inside DI sets that give cost and selling figures. The questions are short, the numbers are friendly, and the only real danger is using the wrong base.

The four terms

Two rules settle most confusion. Profit and loss percentages are on CP unless the question says otherwise. Discount percentages are on MP, always.

The formulas, and why they work

• Profit = SP − CP. Loss = CP − SP.
• Profit % = profit ÷ CP × 100.
• SP = CP × (100 + profit %) ÷ 100, and SP = CP × (100 − loss %) ÷ 100.
• SP = MP × (100 − discount %) ÷ 100.
• Successive discounts of a% and b% give a net discount of a + b − ab/100.

The successive-discount rule is the successive-change rule from percentage with both changes negative. The second discount is taken on an already reduced price, so it removes a little less than b% of the original, which is where the − ab/100 comes from.

The CP = 100 method

When a question gives only percentages, set CP = 100 and follow the chain. Mark-up, discount and profit then read off directly as numbers. Every example below with no rupee values uses this.

Two special results

• Same SP, x% profit on one and x% loss on the other: there is always a net loss of x²/100 per cent. The loss-making item had the higher cost, so the loss outweighs the profit.
• CP of x articles = SP of y articles: profit % = (x − y) ÷ y × 100. If y is larger than x, it is a loss of (y − x) ÷ y × 100.

Worked examples

Example 1. An item is sold for ₹690 at a profit of 15%. Find the cost price.

1. SP = CP × 1.15.
2. CP = 690 ÷ 1.15 = ₹600. Check: 15% of 600 is 90, and 600 + 90 = 690.

Example 2. A shopkeeper marks goods 40% above cost and gives a 20% discount. Find the profit percentage.

1. CP = 100. MP = 140.
2. SP = 140 × 0.8 = 112.
3. Profit = 12%.

Example 3. How much above cost should an item be marked so that after a 10% discount the seller still makes 17% profit?

1. CP = 100, so the required SP = 117.
2. SP = MP × 0.9, so MP = 117 ÷ 0.9 = 130.
3. Mark it 30% above cost.

Example 4. Two phones are sold for ₹1,200 each. One is sold at a 20% profit and the other at a 20% loss. Find the overall result.

1. Shortcut: loss = 20²/100 = 4%.
2. Check with rupees: CP of the first = 1,200 ÷ 1.2 = 1,000; CP of the second = 1,200 ÷ 0.8 = 1,500.
3. Total CP = 2,500, total SP = 2,400. Loss = 100, which is 4% of 2,500.

Example 5. The cost price of 20 pens equals the selling price of 16 pens. Find the profit percentage.

1. Let each pen cost ₹1. Then 16 pens sell for ₹20, so one pen sells for 20/16 = 1.25.
2. Profit = 25%. The formula gives (20 − 16) ÷ 16 × 100, the same answer.

Example 6. A shopkeeper claims to sell at cost price but uses a 900 g weight in place of 1 kg. Find the gain.

1. For every 900 g handed over, the shopkeeper charges for 1,000 g.
2. Gain = 100 ÷ 900 × 100 = 11.11%.
3. The base is 900 because that is what the seller actually gave, which is the true cost.

Common mistakes

• Calculating profit % on SP instead of CP.
• Calculating discount on CP instead of MP.
• Adding successive discounts: 20% and 10% is 28%, not 30%.
• Assuming equal profit and loss percentages cancel out when the SPs are equal.
• In false-weight questions, using the claimed weight as the base.

Practice

Set a 5-minute timer.

1. CP ₹250, SP ₹300. Profit %?
2. An item sold for ₹510 gives a loss of 15%. Find the CP.
3. Successive discounts of 20% and 15%. Net discount?
4. Goods are marked 50% above cost and sold at a 20% discount. Profit %?
5. An item marked ₹1,500 is sold at a 12% discount, and the seller still gains 10%. Find the CP.
6. The CP of 12 articles equals the SP of 15 articles. Find the profit or loss %.
7. Two items are sold for ₹990 each, one at a 10% profit and one at a 10% loss. Find the overall result in rupees.
8. A dealer uses an 800 g weight for 1 kg and sells at cost price. Find the gain %.

Answers:

1. 20%. 50 ÷ 250 × 100.
2. ₹600. 510 ÷ 0.85.
3. 32%. 20 + 15 − (20 × 15)/100 = 35 − 3.
4. 20%. CP 100, MP 150, SP 120.
5. ₹1,200. SP = 1,500 × 0.88 = 1,320; CP = 1,320 ÷ 1.1.
6. 20% loss. Each article costs ₹1, so 15 articles sell for ₹12 and each sells for 0.8. Formula: (15 − 12) ÷ 15 × 100.
7. Loss of ₹20. CPs are 990 ÷ 1.1 = 900 and 990 ÷ 0.9 = 1,100, total 2,000. SP total 1,980. The loss is 1%, as the x²/100 rule predicts.
8. 25%. 200 ÷ 800 × 100.

What to do next

• Write the base table from memory until you can reproduce it without looking.
• Solve ten questions with CP = 100, then ten with rupee values, and compare your times.
• Revise percentage, which this topic depends on, and move on to simple and compound interest.
• Try partnership next, which uses the same "share of profit" thinking.