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The price of diesel is increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption ?1. 9.5%2. 6.5%3. 7.2%4. 8.7% |
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Answer» Correct Answer - Option 4 : 8.7% Given: Percentage increase in the price of diesel = 26% Percentage increase in total expenditure = 15% Concept used: P × C = E Where P is Price, C is Consumption and E is expenditure Calculation: Let initial price be P1, consumption be C1, and expenditure be E1 P1 × C1 = E1 ⇒ C1 = E1/P1 Let new price be P2, new quantity consumed be C2, and new expenditure be E2 P2 = P1 + 26% of P1 ⇒ P2 = 1.26P1 E2 = E1 + 15% of E1 ⇒ E2 = 1.15E1 As, P2 × C2 = E2 ⇒ 1.26P1 × C2 = 1.15E1 ⇒ C2 = (1.15E1)/(1.26P1) ⇒ C2 = 0.9126 × E1/P1 ⇒ C2 = 0.9126C1 Decrease in consumption = C1 – C2 ⇒ Decrease in consumption = C1 – 0.9126C1 = 0.0874C1 Percentage decrease in consumption = (Decrease in consumption/Initaial consumption) × 100 ⇒ Percentage decrease in consumption = (0.0874C1/C1) × 100 ∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place) |
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