The price of a wire made of a superalloy material is proportional to the square of its length

Q. The price of a wire made of a superalloy material is proportional to the square of its length. The price of 10 m length of the wire is Rs. 1600. What would be the total price (in Rs.) of two wires of lengths 4 m and 6m?

(A) 768            (B) 832            (C) 1440          (D) 1600

Ans: 832

The price of wire made of super alloy material is proportional to the square of its length.

Price × (length)2

Price = k × l2

Length of wire = 10 m

According to given condition,

1600 = k (10)2 ⇒ 1600 = k (100) ⇒ k = 16

So that price of two wires of length 4 m and 6 m is = k [l²1 + l²2] = 16[4² + 6²]

Total cost = 832