Rice is now being sold at Rs. 29 per kg. During the last month, its cost was Rs. 25 per kg. By how much percentage should a family reduce its consumption, so as to keep the expenditure the same as before? (correct to nearest integer)

Answer: Option A

Given:
New selling price = Rs. 29 per kg
Old selling price = Rs. 25 per kg
Expenditure = constant
Formula used:
(i) Expenditure = Price × Quantity
(ii) Percentage difference = $$\frac{\text{New price}-\text{Old price}}{\text{Old price}}\times 100$$
Calculations:
Let expenditure, initial selling price and initial quantity be C, P₁ and Q₁ respectively.
C = P₁ × Q₁
⇒ C = 25 × Q₁
⇒ Q₁ = $$\frac{\text{C}}{25}$$
Let final selling price and final quantity be P₂ and Q₂ respectively.
C = P₂ × Q₂
⇒ C = 29 × Q₂
⇒ Q₂ = $$\frac{\text{C}}{29}$$

Percentage difference $$=\frac{{\text{Q}}_2-{\text{Q}}_1}{{\text{Q}}_1}\times 100$$
$$\begin{array}{rl}& \Rightarrow \left[\frac{\frac{\text{C}}{29}-\frac{\text{C}}{25}}{\frac{\text{C}}{25}}\right]\times 100\\ & \Rightarrow \left[\frac{\frac{25\text{C}-29\text{C}}{25\times 29}}{\frac{\text{C}}{25}}\right]\times 100\\ & \Rightarrow \frac{-\left(\frac{4\text{C}}{725}\right)}{\frac{\text{C}}{25}}\times 100\\ & \Rightarrow \frac{-\left(4\text{C}\times \text{25}\right)}{725\text{C}}\times 100\\ & \Rightarrow -13.79\%\approx -14\%\end{array}$$
∴ By 14% should a family reduce its consumption, so as to keep the expenditure the same as before.

Alternate solution
\begin{array}{*{20}{c}} {}&{{\text{Price}}}&{{\text{Consumption}}} \\ {{\text{Old}}}&{25}&{{\mathbf{29}}} \\ {{\text{New}}}&{29}&{{\mathbf{25}}} \\ {{\text{Expenditure}}}&{25 \times 29}&{29 \times 25} \end{array}
Thus, family should reduce their consumption by 4 kg
% Reduction $$=\frac{4}{29}\times 100=13.79\approx 14\%$$
∴ The family should reduce the consumption by 14%.