Four years ago, the ratio of the ages of A and B was 2 : 1. Four years hence, this ratio will become 3 : 2. What is the ratio of their present ages?

Correct option is A

Solution:

Let the present ages of A and B be  x  and  y  respectively.

Four years ago, the ratio of their ages was given as:

​$$\frac{x - 4}{y - 4} = \frac{2}{1}$$​​

This simplifies to:  x - 4 = 2(y - 4)  which gives the equation:

x - 4 = 2y - 8 

Rearranging this, we get the equation:

 x = 2y - 4 

Four years hence, the ratio of their ages will be:

​$$\frac{x + 4}{y + 4} = \frac{3}{2}$$​​

This simplifies to:  2(x + 4) = 3(y + 4) , which gives the equation:

2x + 8 = 3y + 12 

Rearranging this, we get the equation:

 2x - 3y = 4 

Substitute  x = 2y - 4  into the second equation:

2(2y - 4) - 3y = 4 

Simplifying this:

 4y - 8 - 3y = 4 

y - 8 = 4 

Therefore,  y = 12 

Substitute  y = 12  into  x = 2y - 4

x = 2(12) - 4 = 24 - 4 = 20 

Thus, the present ages of A and B are 20 and 12 respectively. Therefore, the ratio of their present ages is:

​$$\frac{20}{12} = \frac{5}{3}$$​​