Profit, Loss and Discount
ICSE Class 7 · Mathematics · Chapter 9
What this chapter covers
- Cost price and selling price
- Profit and loss
- Profit percent and loss percent
- Finding the selling price from the cost price
- Finding the cost price from the selling price
- Marked price and discount
- Discount percent
Key points
- Cost price (CP) is what is paid to buy an article; selling price (SP) is what it is sold for.
- When SP is more than CP there is a profit: Profit = SP − CP.
- When CP is more than SP there is a loss: Loss = CP − SP.
- When SP equals CP there is no profit and no loss.
- Profit percent and loss percent are always worked out on the cost price: Profit% = (Profit ÷ CP) × 100.
- To find SP from CP, add the profit to CP or subtract the loss from CP; in one step, SP = CP × (100 + Profit%) ÷ 100.
- To find CP from SP, treat CP as ₹100 and use the unitary method; never take the percentage of the SP.
- Marked price (MP) is the price on the label; discount is the reduction given on it, and SP = MP − Discount.
- Discount percent is always worked out on the marked price: Discount% = (Discount ÷ MP) × 100.
- A seller can give a discount and still make a profit, because the profit is counted from the CP and the discount from the MP.
- Check every backward answer by working forwards to the price you were given.
Questions answered
What is meant by the cost price of an article, and how is it different from the selling price?
The cost price is the money paid to buy the article. The selling price is the money for which it is sold. The seller's CP is what he paid, and his SP is what he receives.
A shopkeeper buys a lamp for ₹350 and sells it for ₹420. Find his profit.
Profit = 420 - 350 = ₹70.
A cloth merchant buys a sari for ₹900 and sells it for ₹828. Find the loss percent.
Loss = 900 - 828 = ₹72. Loss% = (72)/(900) × 100 = 8%.
Asha makes a profit of ₹60 on a watch that cost her ₹400. Bhavesh makes a profit of ₹45 on a radio that cost him ₹250. Whose deal was better? Give a reason.
Asha's profit percent is (60)/(400) × 100 = 15%. Bhavesh's profit percent is (45)/(250) × 100 = 18%. Bhavesh's deal was better, because he earned more for every ₹100 he spent.
A trader buys a carton of juice for ₹480 and wants a profit of 12(1)/(2)%. At what price should he sell it?
Profit = (1)/(8) × 480 = ₹60, so SP = 480 + 60 = ₹540.
A mobile cover is sold for ₹264 at a profit of 10%. Find its cost price.
CP = 264 × (100)/(110) = ₹240. Check: 10% of ₹240 is ₹24, and 240 + 24 = 264.
Kunal says: "I sold my old cycle for ₹450 at a loss of 10%, so it must have cost me 450 + 45 = ₹495." Is he right? Explain.
No. The 10% loss is on the cost price, not on the selling price. If CP is ₹100, SP is ₹90, so CP = 450 × (100)/(90) = ₹500. Check: 10% of ₹500 is ₹50, and 500 - 50 = 450.
A dress marked ₹600 is sold at a discount of 18%. Find the discount and the selling price.
Discount = (18)/(100) × 600 = ₹108. SP = 600 - 108 = ₹492.