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%
1. 9.5%
2. 6.5%
3. 7.2%
4. 8.7%
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)