Resulting alloy ratio after mixing – UGC NET Question

In the first alloy, copper and zinc are 7/10 and 3/10 of the weight respectively. In the second alloy, copper and zinc are 5/7 and 2/7 of the weight respectively. Taking equal weights of each alloy, total copper = 7/10 + 5/7 = (49 + 50)/70 = 99/70 and total zinc = 3/10 + 2/7 = (21 + 20)/70 = 41/70. The common denominator 70 cancels in the ratio, so copper:zinc = 99:41.

Option A:
Option A, 89:41, looks close to the correct ratio but uses 89 instead of 99, indicating an incorrect sum of copper fractions. To obtain 89, one would have to miscalculate either 7/10 or 5/7, and using this ratio would not respect the exact contributions from both alloys.

Option B:
Option B, 41:99, simply reverses the correct ratio and would imply that zinc is present in much larger proportion than copper in the mixture. This contradicts the original alloys, both of which have more copper than zinc, so 41:99 cannot represent the final proportions.

Option C:
Option C, 99:44, keeps the correct numerator 99 but inflates the zinc component from 41 to 44. This could arise from careless arithmetic in adding 3/10 and 2/7. However, if zinc were 44 parts, the total fractions would no longer sum to the actual combined mixture, so 99:44 is inconsistent with the data.

Option D:
Option D is correct because it is derived from adding the fractional parts for copper and zinc separately and then simplifying the resulting ratio. The common denominator cancels out, leaving 99:41 as the exact composition ratio for the combined alloy when equal weights of each initial alloy are used.