Profit and loss for SSC GD

Profit and loss questions describe simple shop situations: a trader buys something, maybe spends a little on it, and sells it. You need two prices, one rule about percentages and one method for moving between them.

The topic is a direct use of percentage. If percentage increase and decrease feel easy, this chapter will too. It also leads straight into discount, which adds a third price, the marked price.

The terms

The formulas

• Profit % = profit ÷ CP × 100
• Loss % = loss ÷ CP × 100

The multiplier method

This is the fastest way to move between CP and SP.

So a 25% profit means SP = 1.25 × CP, and a 10% loss means SP = 0.9 × CP. When the SP is given and you need the CP, divide by the multiplier. Don't take the percentage of the SP.

Buying and selling in bunches

When items are bought at "x for ₹a" and sold at "y for ₹b", take the LCM of x and y as the number of items. Then both CP and SP come out as whole numbers.

The equal selling price trap

If two items are sold at the same selling price, one at r% profit and the other at r% loss, the trader always makes an overall loss of (r × r ÷ 100)%. It is never "no profit, no loss", because the two cost prices are different.

Solved examples

Example 1. An article bought for ₹4,500 is sold for ₹5,400. Find the profit percentage.

1. Profit = 5,400 − 4,500 = ₹900.
2. Profit % = 900 ÷ 4,500 × 100 = 20%.

Example 2. A trader buys a used scooter for ₹24,000, spends ₹1,000 on repairs and sells it for ₹27,500. Find the profit percentage.

1. Total CP = 24,000 + 1,000 = ₹25,000.
2. Profit = 27,500 − 25,000 = ₹2,500.
3. Profit % = 2,500 ÷ 25,000 × 100 = 10%.

Example 3. An article is sold for ₹1,380 at a profit of 15%. Find its cost price.

1. SP = 1.15 × CP.
2. CP = 1,380 ÷ 1.15 = ₹1,200.
3. Check: 15% of 1,200 = 180, and 1,200 + 180 = 1,380.

Example 4. By selling a watch for ₹2,640, a shopkeeper loses 12%. At what price should it be sold to gain 10%?

1. SP = 0.88 × CP, so CP = 2,640 ÷ 0.88 = ₹3,000.
2. For a 10% gain: SP = 3,000 × 1.1 = ₹3,300.

Example 5. Bananas are bought at 6 for ₹10 and sold at 4 for ₹10. Find the profit percentage.

1. LCM of 6 and 4 is 12. Work with 12 bananas.
2. CP of 12 = 2 × ₹10 = ₹20. SP of 12 = 3 × ₹10 = ₹30.
3. Profit = ₹10 on ₹20 = 50%.

Example 6. Two items are each sold for ₹990. One is sold at a 10% profit and the other at a 10% loss. Find the overall result.

1. CP of the first = 990 ÷ 1.1 = ₹900.
2. CP of the second = 990 ÷ 0.9 = ₹1,100.
3. Total CP = ₹2,000; total SP = ₹1,980.
4. Loss = ₹20, which is 20 ÷ 2,000 × 100 = 1% loss.
5. Shortcut: 10 × 10 ÷ 100 = 1% loss.

Common mistakes

Practice set

1. An article bought for ₹750 is sold for ₹900. Find the profit percentage.
2. An article bought for ₹1,250 is sold for ₹1,100. Find the loss percentage.
3. An item costs ₹640 and is sold at a 25% profit. Find the selling price.
4. An item is sold for ₹1,560 at a 20% profit. Find the cost price.
5. An item is sold for ₹850 at a 15% loss. Find the cost price.
6. Pens are bought at 5 for ₹20 and sold at 4 for ₹20. Find the profit percentage.
7. A cycle is bought for ₹3,600, ₹400 is spent on repairs, and it is sold for ₹4,400. Find the profit percentage.
8. Two phones are each sold for ₹6,000, one at a 20% profit and the other at a 20% loss. Find the overall profit or loss percentage.

Answers:

1. Profit 150; 150 ÷ 750 × 100 = 20%.
2. Loss 150; 150 ÷ 1,250 × 100 = 12%.
3. 640 × 1.25 = ₹800.
4. 1,560 ÷ 1.2 = ₹1,300.
5. 850 ÷ 0.85 = ₹1,000.
6. LCM 20 pens: CP = 4 × 20 = ₹80, SP = 5 × 20 = ₹100. Profit 20 on 80 = 25%.
7. CP = ₹4,000; profit ₹400 = 10%.
8. CPs are 6,000 ÷ 1.2 = ₹5,000 and 6,000 ÷ 0.8 = ₹7,500. Total CP ₹12,500, SP ₹12,000, loss ₹500 = 4% loss.

What to do next

• Write the multiplier table from memory.
• Solve 10 "find the CP" questions, dividing by the multiplier each time.
• Move on to discount, which adds the marked price.
• Revise percentage if the multipliers feel slow.