Question

The price of sugar fell by $10\%$.If the same amount of money has to be spent on sugar as before, by how much per cent must the consumption be increased?

Answer 1

The value of sugar falls$10\%$

Increase in consumption$=$?

Suppose we bought $100$units of sugar for $₹100$.

Due to the fall in price now $100$ units of sugar will be available for $₹90$.

Now for$₹90$, the quantity of sugar available=$100$units

Now for $₹100$, the quantity of sugar available$=\frac{100}{90}\times 100$

$$\begin{gathered} =\frac{1000}{9} \\ =111.11\mathrm{units} \end{gathered}$$

Difference in the consumption$$\begin{gathered} =(111.11-100)\% \\ =11.11\% \end{gathered}$$

Hence, the consumption of sugar is to be increased by $11.11\%$