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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 6 m?
  • a)
    768
  • b)
    832
  • c)
    1440
  • d)
    1600
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The price of a wire made of a superalloy material is proportional to t...

Now total cost = 52k  52 x 16 = 832
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The price of a wire made of a superalloy material is proportional to t...
Given:
- The price of a wire made of a superalloy material is proportional to the square of its length.
- The price of a 10 m length wire is Rs. 1600.

To find:
The total price (in Rs.) of two wires of lengths 4 m and 6 m.

Explanation:
Let's assume the price of the wire per unit length be Rs. p.

According to the given information, the price of a wire is proportional to the square of its length. Mathematically, we can express this as:
Price = k * Length^2

Finding the constant of proportionality (k):
We are given that the price of a 10 m length wire is Rs. 1600.
So, we can substitute these values into the equation to find the constant of proportionality (k):
1600 = k * 10^2
1600 = 100k
k = 1600/100
k = 16

Now we have the value of k, which is 16.

Finding the total price of two wires:
We need to find the total price of two wires of lengths 4 m and 6 m.

Price of the first wire (4 m):
Price = k * Length^2
Price = 16 * 4^2
Price = 16 * 16
Price = 256

Price of the second wire (6 m):
Price = k * Length^2
Price = 16 * 6^2
Price = 16 * 36
Price = 576

Total price of two wires:
Total Price = Price of the first wire + Price of the second wire
Total Price = 256 + 576
Total Price = 832

Therefore, the total price of two wires of lengths 4 m and 6 m is Rs. 832.
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