Question
An alloy is made of metal A and metal B in the ratio
2:3. In each step, we add metals A and B to the alloy equal to 20% and 5% of weights of metal A and metal B respectively at previous step. Which step onwards will the alloy contain more than 50% of metal A?Solution
ATQ, Let's solve the question, The ratio of A and B = 2:3. So, A will be 40%, and B will be 60%. 1st step A = 20% of 40 = 8, B = 5% of 60 = 3 A = 48Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â B = 63 2nd step A = 20% of 48 = 9.6, B = 5% of 63 = 3.15 A = 57.6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â B = 66.15 3rd step A = 20% of 57.6 = 11.40, B = 5% of 66.15 = 3.35 A = 68.40Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â B = 69.50 4th step A = 20% 0f 68.40 = 13.8, B = 5 % 0f 69.50 = 3.5 A = 82.20Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â B = 73 So, in the 4th step, the alloy will contain more than 50% metal. From the 4th step onwards, the alloy will contain more than 50% of metal A.
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