Apply percentages to real-world situations — increases, decreases, and finding the original value from a percentage.
To increase a value by a percentage, add the percentage of the value to itself. To decrease, subtract it. Percentage change = (change in value ÷ original value) × 100.
A price of ₹500 increases by 20%. Find the new price.
20% of 500 = 100, new price = 500 + 100 = ₹600
A population of 8000 decreases by 15%. Find the new population.
15% of 8000 = 1200, new population = 8000 − 1200 = 6800
If you know a value after a percentage change, you can work backward to find the original value by setting up an equation based on what percentage the new value represents.
After a 25% increase, a number becomes 100. Find the original number.
Let original = x. x + 0.25x = 100, so 1.25x = 100, x = 80
After a 10% discount, an item costs ₹450. Find its original price.
Let original = x. x − 0.10x = 450, so 0.90x = 450, x = 500
1. A salary of ₹30000 increases by 8%. Find the new salary.
2. A quantity of 250kg decreases by 12%. Find the new quantity.
3. After a 20% increase, a number becomes 144. Find the original number.
4. After a 15% discount, an item costs ₹680. Find its original price.
5. A student's marks increased from 60 to 75. Find the percentage increase.