Percentage · lesson 14 of 20 · free

Two changes in a row — How to calculate percentage

If a price goes up 10% and then down 10%, is it back where it started? No! The second change is worked out on the new price, which is bigger. Do the changes one at a time — or try a price of ₹100.

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How to work it out

One at a time — “do the first change, then work out the second percent on the new value”

  1. Do the first change: find the percent of the starting value and add it or take it away.
  2. Do the second change on the NEW value, not the starting one.
  3. For the total percent, start with ₹100: two rises of a% and b% make a + b + a × b ÷ 100 percent in all.

Use it for: Prices that change twice, a sale on top of a sale, growth over two years, and Olympiad and Class 8–10 problems.

🧮 Check your own sums with the free Percentage calculator — it shows the working.

Worked example: A price of ₹200 goes up by 30%, and then the new price goes up by 20%. What is the final price, in rupees? → 312

  1. First change: 30% of ₹200 = ₹60, so the price becomes 200 + 60 = ₹260.
  2. The second change is on the NEW price: 20% of ₹260 = ₹52.
  3. Final price = 260 + 52 = 312.

Check: 30 + 20 + 30 × 20 ÷ 100 = 56% in all; 56% of 200 = 112, and 200 + 112 = 312 ✓

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✏️ Practice

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🏁 Lesson 14 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Successive Percentage Change Worksheet

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