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 \(\frac{x}{3}\)%.

32.25

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%