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A is an alloy of tin and copper and B is an alloy of copper and zinc. A has 30% copper while B has 50% copper, x gins of A is mixed with 30 gins of B to form another alloy which has 45% copper. What is the value ofx?
  • a)
    5
  • b)
    10
  • c)
    15
  • d)
    20
Correct answer is option 'B'. Can you explain this answer?
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A is an alloy of tin and copper and B is an alloy of copper and zinc. ...
Given:
- A is an alloy of tin and copper with 30% copper
- B is an alloy of copper and zinc with 50% copper
- x gins of A is mixed with 30 gins of B to form another alloy with 45% copper

To find: Value of x

Approach:
1. Write the equation for the new alloy formed by mixing A and B.
2. Use the given percentage of copper in A and B to form an equation in terms of x.
3. Simplify the equation and solve for x.

Solution:
1. Let's assume that x gins of A is mixed with 30 gins of B to form the new alloy. The total weight of the new alloy will be x + 30 gins.
2. Using the percentage of copper in A and B, we can write the equation for the new alloy as follows:

0.3x + 0.5(30) = 0.45(x + 30)

Explanation:
- The first term on the left side of the equation represents the amount of copper in x gins of A.
- The second term on the left side of the equation represents the amount of copper in 30 gins of B.
- The right side of the equation represents the amount of copper in the new alloy, which is 45% of the total weight.

3. Simplifying the equation:

0.3x + 15 = 0.45x + 13.5

0.15x = 1.5

x = 10

Therefore, the value of x is 10 gins.

Answer: Option B.
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