Question

If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before.

• A. 30%
• B. \(23\frac{1}{3}\)
• C. \(27\frac{2}{13}\)
• D. 19%

Answer 1

The Correct Option is B

Let the initial quantity of ornaments be \(Q\) and the initial price be \(P\). 
\(\therefore\) The total expenditure is \(Q \times P\).

When the price increases by 30%, the new price becomes \(1.3P\). 
To keep the expenditure the same, the new quantity \(Q'\) must satisfy:
\(Q' \times 1.3P = Q \times P\)
\(\Rightarrow\)\(Q' = \frac{Q \times P}{1.3P} = \frac{Q}{1.3}\)

The reduction in quantity is:
\(Q - Q' = Q - \frac{Q}{1.3} = Q \left( 1 - \frac{1}{1.3} \right) = Q \left( \frac{0.3}{1.3} \right) = \frac{3}{13} Q\)

Hence, the percentage reduction is
\(\frac{\frac{3}{13} Q}{Q} \times 100 = \frac{3}{13} \times 100 \approx 23.08\%\)

Therefore, the quantity must be reduced by approximately \(23\frac{1}{13}\%\)