A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A ?

(a) 60%
(b) 45·5%
(c) 40%
(d) 37·5% ✓ UPSC's answer

Why the answer is (d)

• Let the weight of block A be $W_A$ and the weight of block B be $W_B$.

• The problem states that placing B on A increases the weight by 60%, so $W_B = 0.60 W_A$.

• The total weight of A and B is $W_{total} = W_A + W_B = W_A + 0.60 W_A = 1.60 W_A$.

• When B is removed, the weight reduction is equal to the weight of B, which is $W_B$.

• The percentage reduction with respect to the total weight is calculated as $(W_B / W_{total}) \times 100$.

• Substituting the values: $(0.60 W_A / 1.60 W_A) \times 100 = (0.60 / 1.60) \times 100 = 37.5\%$.

Why the other options are wrong

(a) 60%: 60% is the increase relative to A alone, not the reduction relative to the combined total weight.
(b) 45·5%: 45.5% is an incorrect calculation that does not follow from the ratio of B to the total weight (0.6/1.6).
(c) 40%: 40% is an incorrect calculation that does not follow from the ratio of B to the total weight (0.6/1.6).

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.