deepak268 wrote:
12kgs of alloy1 has P1% of iron in it. 6 kgs of alloy2 has P2% iron in it ( P1 not equal to P2). X kgs of each alloy is cut and then fused with the remaining part of the other alloy. If two resulting alloys have equal percentage of iron, find X?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Let us consider the final percentage of iron be P3.
We can form the following two equations from the information given:
For Iron content in 1st Alloy A
(12 - X) * P1 + X * P2 = 12 * P3
For Iron content in 1st Alloy B
(6 - X) * P2 + X * P1 = 6 * P3
=> (6 - X) * 2 * P2 + X * 2 * P1 = 12 * P3
Now equating both the equations we get:
(12 - X) * P1 + X * P2 = (6 - X) * 2 * P2 + X * 2 * P1
12P1 - XP1 + XP2 = 12P2 - 2XP2 + 2XP1
=> 12P1 - 12P2 = 3XP1 - 3XP2
=> 4 * (P1 - P2) = X (P1 - P2)
=> X = 4
Hence D is the correct answer.
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