The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is :

(a) 16 : 13
(b) 5 : 4
(c) 7 : 5
(d) 12 : 11 ✓ UPSC's answer

Why the answer is (d)

• Let the basic pay of the first person be B1 and the second person be B2.

• The total emoluments for the first person are B1 + 0.65B1 = 1.65B1.

• The total emoluments for the second person are B2 + 0.80B2 = 1.80B2.

• Since the total emoluments are equal, 1.65B1 = 1.80B2.

• The ratio B1/B2 is calculated as 1.80/1.65, which simplifies to 180/165.

• Dividing both numerator and denominator by 15 gives the ratio 12:11, matching option (d).

Why the other options are wrong

(a) 16 : 13: The ratio 16:13 does not result from the correct calculation of 1.80/1.65.
(b) 5 : 4: The ratio 5:4 is incorrect because it does not account for the specific allowance percentages of 65% and 80%.
(c) 7 : 5: The ratio 7:5 is incorrect as it does not match the derived proportion of total emoluments to basic pay.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.