​Four years ago, the ratio of the age of Ram to that of Shyam was 13 : 9. Eight years from now, their ages will be in the ratio 4 : 3. The difference (in years) between their present ages is:​

Correct option is B

Given:

Four years ago, the ratio of Ram's age to Shyam's age was 13 : 9.

Eight years from now, their ages will be in the ratio 4 : 3

Solution:

Four years ago, the ratio of their ages was 13:913 : 913:9 This gives:

​$$\frac{x-4}{y-4}=\frac{13}{9}$$

9(x - 4) = 13(y - 4)

​$$9x-36=13y-52$$9x−13y=−16(1)9x - 13y = -16 \tag{1}

9x − 13y =  −16 .......(1)

Eight years from now, the ratio of their ages will be $$4:3$$. This gives:

$$\frac{x+8}{y+8}=\frac{4}{3}$$​

3(x+8) = 4(y+8)

​$$3x+24=4y+32$$3x−4y=8(2)3x - 4y = 8 \tag{2}

3x − 4y = 8 .....(2)

From equation (1) and (2) ,

x = 56 ,y = 40

x - y = 56 - 40  = 16

The difference between their present ages is 16 years.

Thus, correct answer is option (B).