Question : The price of onion increases by 12.5%. The consumption of onion also increases by 12.5%. What is the approximate percentage increase in the expenditure on account of the purchase of onions?
Option 1: 29.12%
Option 2: 24.82%
Option 3: 28.44%
Option 4: 26.56%
Correct Answer: 26.56%
Solution :
Given,
Price of onion increases = 12.5%
Consumption of onion increases = 12.5%
We know,
Expenditure = Price × Consumption
Let the original price and consumption be Rs 100 and 100 kg respectively
⇒ New price of onion after 12.5% increase $= 100+ \frac{(100 × 12.5 )}{ 100}=100 + 12.5=112.5$
⇒ New consumption of onion after 12.5% increase $= 100+ \frac{(100 × 12.5 )}{ 100}=100 + 12.5=112.5$ kg
⇒ Original Expenditure = Original Price × Original Consumption = 100 × 100 = 10000 Rs/ kg
⇒ New Expenditure = New Price × New Consumption = 112.5 × 112.5 = 12656.25 Rs/kg
⇒ Increase in Expenditure = (12656.25 – 10000) = 2656.25 Rs/kg
⇒ % change in Expenditure = $\frac{\text{Increase in Expenditure}}{\text{Original Expenditure}} × 100=\frac{ 2656.25}{10000}× 100= 26.56\%$
Hence, the correct answer is 26.56%.
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