The ratio of male to female workers in two companies A and B is 13 : 10 and 7 : 5, respectively. If both the companies have the same number of female workers, then what is the ratio of the total number of workers in A to those in B?

(a) 24 : 23
(b) 23 : 24 ✓ UPSC's answer
(c) 18 : 17
(d) 27 : 18

Why the answer is (b)

• Let the number of female workers in both companies be a common multiple of 10 and 5, which is 10.

• In Company A, the ratio of male to female is 13:10, so if females are 10, males are 13, making the total workers 13 + 10 = 23.

• In Company B, the ratio of male to female is 7:5, so if females are 5, males are 7. To match the female count of 10, multiply the ratio by 2, giving 14 males and 10 females.

• The total workers in Company B are 14 + 10 = 24.

• The ratio of total workers in A to B is therefore 23 : 24.

Why the other options are wrong

(a) 24 : 23: This option inverts the correct ratio of 23:24.
(c) 18 : 17: This ratio does not correspond to the calculated totals of 23 and 24.
(d) 27 : 18: This ratio is mathematically incorrect based on the given male-to-female proportions.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.