Rohan's present age is $$\frac37$$​ times of the age of his mother. After five years, he will be one- half of the age of his mother. How old is his mother at present ?

Correct option is C

Given:

Rohan's present age =$$\frac{3}{7}$$​ times his mother's present age.

After 5 years, Rohan will be half of his mother's age.

Solution:

Let Rohan's present age be R and his mother's present age be M .

From the given information:
R = $$\frac{3}{7} \times M \quad \text{(Rohan's present age in terms of his mother's age)}.$$​​
After 5 years:
R + 5 = $$\frac{1}{2} \times (M + 5).$$​​

Using the first equation, substitute R =$$\frac{3}{7} \times$$​M  into the second equation:

$$\left(\frac{3}{7} \times M\right) + 5 = \frac{1}{2} \times (M + 5). \\ \ \\2 \left(\frac{3}{7} \times M + 5\right) = M + 5.\\ \ \\\frac{6}{7} \times M + 10 = M + 5.\\ \ \\\frac{6}{7} \times M - M = -5.\\ \ \\\left(\frac{6}{7} - 1\right) \times M = -5,\\ \ \\\frac{-1}{7} \times M = -5.$$​

M = 35.

Thus, Rohan's mother is 35 years old at present.