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)

Solution (By Examveda Team)

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 $$ = \frac{{{{\text{Q}}_2} - {{\text{Q}}_1}}}{{{{\text{Q}}_1}}} \times 100$$
$$\eqalign{ & \Rightarrow \left[ {\frac{{\frac{{\text{C}}}{{29}} - \frac{{\text{C}}}{{25}}}}{{\frac{{\text{C}}}{{25}}}}} \right] \times 100 \cr & \Rightarrow \left[ {\frac{{\frac{{25{\text{C}} - 29{\text{C}}}}{{25 \times 29}}}}{{\frac{{\text{C}}}{{25}}}}} \right] \times 100 \cr & \Rightarrow \frac{{ - \left( {\frac{{4{\text{C}}}}{{725}}} \right)}}{{\frac{{\text{C}}}{{25}}}} \times 100 \cr & \Rightarrow \frac{{ - \left( {4{\text{C}} \times {\text{25}}} \right)}}{{725{\text{C}}}} \times 100 \cr & \Rightarrow - 13.79\% \approx - 14\% \cr} $$
∴ 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%.