The present age of a father is 1$$\frac12$$​ times the sum of the present ages of his two sons. Six years hence, the ratio of his age to the sum of the ages of his sons will be 6:5. The present age of the father is:

Correct option is C

Present age of father = 1.5× sum of present ages of his two sons.

After 6 years, the ratio of father's age to the sum of sons' ages = 6 : 5

Solution:

Let the sum of the present ages of the two sons be S 

From the first condition:

F = $$1.5 \times S = \frac{3}{2}S .....\tag{1}$$​​

After 6 years, the father’s age and sons’ ages will be:

F + 6 and S + 12

From the second condition:

​$$\frac{F + 6}{S + 12} = \frac{6}{5}...... \tag{2}$$​​

Substitute F = $$\frac{3}{2}$$​S into equation (2):

​$$\frac{\frac{3}{2}S + 6}{S + 12} = \frac{6}{5}$$​​

​$$\left(\frac{3}{2}S + 6\right) = 6(S + 12)$$​​

​$$\frac{15}{2}S + 30 = 6S + 72$$​​

15S + 60 = 12S + 144

15S - 12S = 144 - 60

3S = 84

S = 28

Thus, Father age

F = $$\frac{3}{2} \times 28$$ = 42 years