Question : The price of diesel increased by 16%. A person wants to increase his expenditure on diesel by 10% only. By what percentage, correct to one decimal place, should he reduce his consumption?
Option 1: 6.5%
Option 2: 5.2%
Option 3: 3.7%
Option 4: 4.5%
Correct Answer: 5.2%
Solution : Let the price of diesel and quantity be Rs.100 and 100 litres. Total expenditure = Rs.100 × 100 = Rs.10000 The price of diesel increased by 16%. New price = 100 + 16 = 100 He wants to increase his expenditure on diesel by 10% only. Increased expenditure = Rs.10000 × $\frac{110}{100}$ = 11000 $\therefore$ New consumption of diesel = $\frac{11000}{116}$ = 94.8 litres ⇒ Percentage decreased in consumption = $\frac{(100 - 94.8)}{100}× 100 = 5.2\%$ Hence, the correct answer is 5.2%.
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