If the price of petrol increases by x% but consumption of petrol decreases by x% due to which total expenditure decreases by 20.25%. Find the percentage change in the expenditure, if price and consumption both increase by \(\frac{x}{3}\)%.
Answer & explanation
Correct answer: option 2
Expenditure = Price × consumption
If price increases and consumption decreases then total expenditure decreases by \(\frac{x^2}{100}\) (if both are x%) by successive percentage.
Decrement = -\(\frac{x^2}{100}\)
-\(\frac{x^2}{100}\) = 20.25%
x2 = \(\sqrt {2025}\) (- sign after decrement)
x = 45%
If price and consumption both will increase by \(\frac{x}{3}\)% then change in exp. is → \(\frac{45}{3}\) + \(\frac{45}{3}\) + \(\frac{\frac{45}{3} × \frac{45}{3}}{100}\)
= 15 + 15 + \(\frac{225}{100}\)
= 32.25%