The ratio of the present ages of a husband and a wife is 5:4. Which of the following can be a possible ratio of their ages 20 years ago?a.23:20b.5:4c.13:10d.6:5

The problem states that the current age ratio of the husband to the wife is 5:4. If we subtract 20 years from each of their ages, the ratio should still make sense (i.e., result in whole numbers) because age is a discrete quantity.

Let's denote the husband's age as 5x and the wife's age as 4x.

20 years ago, their ages would be 5x-20 and 4x-20 respectively.

Now, let's check each of the options:

a) 23:20 - If we equate 5x-20/4x-20 = 23/20, we get a quadratic equation that does not result in a whole number solution for x. So, this option is not possible.

b) 5:4 - This is the current ratio, not the ratio 20 years ago. So, this option is not possible.

c) 13:10 - If we equate 5x-20/4x-20 = 13/10, we get a quadratic equation that does not result in a whole number solution for x. So, this option is not possible.

d) 6:5 - If we equate 5x-20/4x-20 = 6/5, we get a quadratic equation that results in a whole number solution for x. So, this option is possible.

Therefore, the only possible ratio of their ages 20 years ago is 6:5.