Solve multi-step business problems involving successive discounts, and profit/loss expressed as a fraction of cost or selling price.
When two discounts are applied one after another, the second discount is calculated on the already-reduced price, not the original price. This means two successive discounts don't simply add together.
An item marked ₹1000 gets a 10% discount, then a further 5% discount. Find the final price.
After 10%: 1000 − 100 = 900. After 5% on 900: 900 − 45 = ₹855
Are successive discounts of 20% and 10% the same as a single 30% discount?
No — successive 20% then 10% gives a final price of 0.80 × 0.90 = 72% of original, which is a 28% discount overall, not 30%
Sometimes a problem describes cost price as a fraction of selling price, or vice versa. Setting up the relationship as an equation makes it possible to find the profit or loss percentage.
The cost price of an article is 4/5 of its selling price. Find the profit or loss percent.
Let SP = 5, so CP = 4. Profit = SP − CP = 1. Profit% = (1/4) × 100 = 25%
A shopkeeper sells goods at 90% of the cost price. Find the loss percent.
Let CP = 100, SP = 90. Loss = 10. Loss% = (10/100) × 100 = 10%
1. An item marked ₹2000 gets a 15% discount, then a further 10% discount. Find the final price.
2. Are successive discounts of 10% and 10% the same as a single 20% discount?
3. The cost price of an article is 3/4 of its selling price. Find the profit percent.
4. A shopkeeper sells goods at 80% of the cost price. Find the loss percent.
5. An article marked ₹1500 is sold after two successive discounts of 20% and 5%. Find the final selling price.