The price (per litre) of petrol increases by 75%. By what percent should its consumption be reduced such that the expenditure on it increases by 47% only?

Correct option is A

Given:

The price of petrol increases by 75%.
The expenditure on petrol increases by 47%.
Formula Used:
Expenditure = Price × Consumption
Solution:
Let the original price of petrol be  P and the original consumption be  C.
Original expenditure =$$P \times C .$$​
After the price increase:
New price = P + 0.75P = 1.75P 
Let the new consumption be C' .
New expenditure =$$1.75P \times C'.$$​
New expenditure = Original expenditure + 47% of original expenditure
​$$1.75P \times C' = 1.47\times (P \times C) .$$​​
C' =$$0.84 \times C$$​ 
Reduction = C - C' = C - 0.84C = 0.16C .
Percentage reduction =$$\frac{0.16C}{C} \times 100\% = 16\%$$

Alternate Method:

The price of petrol increases by 75%.

Then, 100 + 75 = 175

The expenditure on petrol increases by 47%.

100 + 47 = 147

So, Reduction= 175 - 147 = 28

Percentage reduction =$$\frac{28}{175}\times 100 = 16\%$$