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An alloy X contains by weight copperandt...

An alloy X contains by weight copperandtin in the ration 7 : 3 and alloy Y contain copperandtin in the ratio 3 : 2. X and Y are taken in the ratio 4 : 1 and melted to form alloy Z. The percentage of copperin alloy Z is:

A

70

B

56

C

65

D

68

Text Solution

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The correct Answer is:
To solve the problem step by step, we will calculate the percentage of copper in the newly formed alloy Z from alloys X and Y. ### Step 1: Determine the composition of alloys X and Y. - Alloy X has copper and tin in the ratio 7:3. - Alloy Y has copper and tin in the ratio 3:2. ### Step 2: Calculate the total parts and the fraction of copper in each alloy. - For Alloy X: - Total parts = 7 + 3 = 10 - Fraction of copper in X = 7/10 - For Alloy Y: - Total parts = 3 + 2 = 5 - Fraction of copper in Y = 3/5 ### Step 3: Convert the fraction of copper in Alloy Y to a common denominator. - The common denominator for 10 and 5 is 10. - Convert the fraction of copper in Y: - Fraction of copper in Y = 3/5 = (3 * 2)/(5 * 2) = 6/10 ### Step 4: Determine the ratio in which alloys X and Y are mixed to form alloy Z. - Alloys X and Y are mixed in the ratio 4:1. - This means for every 4 parts of X, there is 1 part of Y. ### Step 5: Calculate the total parts of the new alloy Z. - If we take 4 parts of X and 1 part of Y, the total parts = 4 + 1 = 5 parts. ### Step 6: Calculate the total amount of copper in alloy Z. - Amount of copper from 4 parts of X: - Copper from X = 4 parts * (7/10) = 28/10 = 28 units of copper. - Amount of copper from 1 part of Y: - Copper from Y = 1 part * (6/10) = 6/10 = 6 units of copper. - Total copper in alloy Z = Copper from X + Copper from Y = 28 + 6 = 34 units of copper. ### Step 7: Calculate the total weight of alloy Z. - Total weight of alloy Z = Total parts = 5 parts (from X and Y combined). ### Step 8: Calculate the percentage of copper in alloy Z. - Percentage of copper in alloy Z = (Total copper in Z / Total weight of Z) * 100 - Percentage of copper = (34 / 50) * 100 = 68%. ### Final Answer: The percentage of copper in alloy Z is **68%**. ---
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