Question

The cost of a pair of shoes varies directly as the square of its size. If a pair of size 5 costs Rs. 500, what is the cost of a pair of size 7?

• A. Rs. 960
• B. Rs. 980
• C. Rs. 1000
• D. Rs. 1020

Hint:

For direct variation problems, establish the constant of proportionality and apply it to the new value.

Answer 1

The Correct Option is B

Cost \( C \propto s^2 \), where \( s \) is the size. 
Given: Size 5 costs Rs. 500, so \( C = k \cdot 5^2 = 500 \Rightarrow k = \frac{500}{25} = 20 \). 
For size 7: 
\[ C = 20 \cdot 7^2 = 20 \cdot 49 = 980 \] Thus, the answer is Rs. 980.