Answer :
The maximum weight that can be achieved without exceeding 178 kgs, using the given weights, is 172 kgs using the combination of weights 77, 48, and 47 kgs. Therefore, the correct option is A.
To find the maximum weight that can be weighed using the given weights (47, 46, 43, 48, 49, 42, and 77 kgs) without exceeding 178 kgs, we need to combine the weights in such a way that their total sum is as close as possible to 178 kgs without going over it. We have to try different combinations to find the maximum sum.
Step-by-step Explanation:
Start with the largest weight, which is 77 kgs.
Add the next largest weight that does not exceed 178 kgs when added to 77 kgs. That would be 49 kgs (77 + 49 = 126 kgs).
Continue adding the next largest weight to the sum without exceeding 178 kgs.
The combinations that provide the largest sum under 178 kgs would be 77 + 49 + 46 + 1 or 77 + 49 + 43 + 4, both totaling 173 kgs, which is not listed as an option.
The largest weight less than 178 kgs that is closest to the options provided is 172 kgs, which can be obtained by using the combination of 77 + 48 + 47 kgs.
Therefore, the correct answer is (a) 172 kgs.
