Question
The price of an item is first increased by 20% and then
decreased by 20%. If the final price is Rs 1,152, what was the original price?Solution
Let original price = P. After 20% increase: Price₁ = P × (1 + 20/100) = P × 120/100 = 6P/5 After 20% decrease on this: Price₂ = Price₁ × (1 − 20/100) = (6P/5) × 80/100 = (6P/5) × 4/5 = 24P/25 Given final price = 1,152: 24P/25 = 1,152 ⇒ 24P = 1,152 × 25 1,152 × 25 = (1,152 × 100)/4 = 115,200 / 4 = 28,800 So 24P = 28,800 P = 28,800 / 24 = 1,200 Answer: Original price = Rs 1,200.
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