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?

Correct Option: (b) 23 : 24

Let the ratio of male to female workers in company A be 13x : 10x, so female workers in A = 10x and male workers = 13x. Total workers in A = 23x. Let the ratio of male to female workers in company B be 7y : 5y, so female workers in B = 5y and male workers = 7y. Total workers in B = 12y. Given that both companies have the same number of female workers, 10x = 5y, which means y = 2x. We need the ratio of the total number of workers in A to those in B. Total workers in A = 23x. Total workers in B = 12y = 12(2x) = 24x. The ratio of total workers in A to B is 23x : 24x = 23 : 24. Thus, option (b) is correct.