Question:medium

An alloy is prepared by mixing three metals A, B and C in the proportion 3: 4: 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5: 2: 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

Updated On: Jan 15, 2026
  • 70
  • 96
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The Correct Option is D

Solution and Explanation

Provided Data:

  • The ratio of volumes for metals A, B, and C is 3:4:7.
  • The ratio of densities (weight per unit volume) for metals A, B, and C is 5:2:6.
  • The combined weight of the alloy is 130 kg.

Assuming a common volume unit denoted by \( x \), the weights are calculated as follows:

Weight of A = \( 3x \times 5 = 15x \)

Weight of B = \( 4x \times 2 = 8x \)

Weight of C = \( 7x \times 6 = 42x \)

The total weight of the alloy is the sum of individual weights:

\[ 15x + 8x + 42x = 65x \]

Given that the total weight is 130 kg:

\[ 65x = 130 \]

Solving for \( x \):

\[ x = \frac{130}{65} = 2 \]

The weight of Metal C is determined by:

\[ \text{Weight of C} = 42x = 42 \times 2 = \boxed{84 \text{ kg}} \]

✅ Final Answer: 84 kg

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