A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?

(a) 10 kg ✓ UPSC's answer
(b) 15 kg
(c) 20 kg
(d) 25 kg

Why the answer is (a)

• Let the weight of the empty vessel be $V$ kg and the weight of the water when full be $W$ kg.

• The total weight when full is given as $V + W = 40$ kg.

• When the vessel is one-third filled, the weight of the water is $\frac{1}{3}W$, so the total weight is $V + \frac{1}{3}W = 20$ kg.

• Subtract the second equation from the first: $(V + W) - (V + \frac{1}{3}W) = 40 - 20$.

• This simplifies to $\frac{2}{3}W = 20$, which gives $W = 30$ kg.

• Substituting $W = 30$ into the first equation: $V + 30 = 40$, so $V = 10$ kg.

Why the other options are wrong

(b) 15 kg: 15 kg is incorrect because it does not satisfy the condition that one-third of the water weight plus the vessel weight equals 20 kg.
(c) 20 kg: 20 kg is incorrect because if the vessel weighed 20 kg, the full water weight would be 20 kg, making the one-third filled weight 26.67 kg, not 20 kg.
(d) 25 kg: 25 kg is incorrect because if the vessel weighed 25 kg, the full water weight would be 15 kg, making the one-third filled weight 30 kg, not 20 kg.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.