An alloy piece of two metals A and B weighs 15 g and is worth Rs. 150. If the weights of A and B are interchanged, the new alloy would be worth Rs. 120. Given price of A is Rs. 6 per g, find the weight of the other metal (B) in the original alloy.

Introduction / Context:
The alloy's value is the sum of values contributed by each metal (price * weight). Interchanging weights creates a second equation. Solve the two linear equations to find the unknown weight of metal B initially.

Given Data / Assumptions:

• Total weight = 15 g.
• First alloy value = Rs. 150.
• Second (weights swapped) value = Rs. 120.
• Price of A = Rs. 6 per g; price of B = unknown p.

Concept / Approach:
Let initial weights be a (A) and b (B). Then a + b = 15. Equations: 6a + p b = 150 and 6b + p a = 120. Add to eliminate asymmetry and find p. Then solve for a and b.

Step-by-Step Solution:
(6a + p b) + (6b + p a) = 270 ⇒ (6 + p)(a + b) = 270Since a + b = 15 ⇒ 15(6 + p) = 270 ⇒ 6 + p = 18 ⇒ p = 12Use 6a + 12b = 150 with a + b = 15Multiply the second by 6: 6a + 6b = 90 ⇒ subtract ⇒ 6b = 60 ⇒ b = 10 g

Verification / Alternative check:
With b = 10, a = 5. Values: first = 6*5 + 12*10 = 30 + 120 = 150; swapped = 6*10 + 12*5 = 60 + 60 = 120.

Why Other Options Are Wrong:
Other weights fail one or both value equations and do not maintain total 15 g.

Common Pitfalls:
Assuming the prices are swapped instead of weights; the problem states interchanging weights.

Final Answer:
10 gms