There is a milk sample with 50% water in it. If 1/3ʳᵈ of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to

(a) 25% ✓ UPSC's answer
(b) 30%
(c) 35%
(d) 40%

Why the answer is (a)

• Let the initial volume of the milk sample be 3 units, which contains 1.5 units of water (50%) and 1.5 units of milk.

• One-third of this sample is taken, which equals 1 unit of the mixture.

• This 1 unit contains 0.5 units of water and 0.5 units of milk.

• This 1 unit is added to an equal amount (1 unit) of pure milk, which contains 0 units of water and 1 unit of milk.

• The new total volume is 1 + 1 = 2 units, and the total water content is 0.5 + 0 = 0.5 units.

• The percentage of water in the new mixture is (0.5 / 2) * 100 = 25%, which corresponds to option (a).

Why the other options are wrong

(b) 30%: 30% is incorrect because the calculation of water content in the final 2-unit mixture yields 25%, not 30%.
(c) 35%: 35% is incorrect as it does not match the derived water percentage of 25% from the 0.5 units of water in 2 units of total mixture.
(d) 40%: 40% is incorrect because the dilution with pure milk reduces the water percentage from 50% to 25%, not 40%.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.