The average rainfall in a city for the first four days was recorded to be 0·40 inch. The rainfall on the last two days was in the ratio of 4 : 3. The average of six days was 0·50 inch. What was the rainfall on the fifth day?

(a) 0·60 inch
(b) 0·70 inch
(c) 0·80 inch ✓ UPSC's answer
(d) 0·90 inch

Why the answer is (c)

• Calculate the total rainfall for the first four days: 4 days × 0.40 inch/day = 1.60 inches.

• Calculate the total rainfall for all six days: 6 days × 0.50 inch/day = 3.00 inches.

• Determine the combined rainfall for the last two days (5th and 6th): 3.00 - 1.60 = 1.40 inches.

• Let the rainfall on the 5th day be 4x and on the 6th day be 3x, based on the given ratio of 4:3.

• Solve for x: 4x + 3x = 1.40, which simplifies to 7x = 1.40, so x = 0.20.

• Calculate the rainfall on the 5th day: 4x = 4 × 0.20 = 0.80 inch, matching option (c).

Why the other options are wrong

(a) 0·60 inch: 0.60 inch is incorrect because it does not satisfy the 4:3 ratio when combined with the remaining rainfall to reach the 6-day total.
(b) 0·70 inch: 0.70 inch is incorrect because it implies a 6th day rainfall of 0.70 inch, which violates the 4:3 ratio (7:7 is 1:1).
(d) 0·90 inch: 0.90 inch is incorrect because it would require a 6th day rainfall of 0.50 inch, resulting in a ratio of 9:5, not 4:3.

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.