Question

The cost of a rectangular glass piece is directly proportional to its length and inversely proportional to its width. If its length is increased by \(40\%\), then by what percentage should its width be decreased so that its cost becomes twice?

• A. 25
• B. 30
• C. 24
• D. 20

Answer 1

The Correct Option is B

Glass Cost Calculation 

Let the original length and width of the glass be L and W, respectively.

The cost of the glass is directly proportional to its length and inversely proportional to its width. Thus,

\[ C \propto \frac{L}{W} \]

When the length is increased by 40%, the new length becomes:

\[ L_{new} = 1.4L \]

Let the new width be \( W_{new} \). If the new cost becomes twice the original cost, we have:

\[ 2C = \frac{1.4L}{W_{new}} \]

Since the original cost is \( C = \frac{L}{W} \), equating the two costs:

\[ 2 \times \frac{L}{W} = \frac{1.4L}{W_{new}} \]

Simplifying,

\[ \frac{2}{1} = \frac{1.4W}{W_{new}} \]

Solving for \( W_{new} \):

\[ W_{new} = \frac{1.4W}{2} = 0.7W \]

The new width is 70% of the original width. Thus, the width is decreased by:

\[ 100\% - 70\% = 30\% \]

Conclusion: The width should be decreased by 30%.

The correct answer is: (b) 30%.