At present Suresh's age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Suresh and his daughter will be 23 : 13. What is the present age of Suresh ?
Correct Answer: 40 years
Let daughter's age be x years.
Suresh's age = 2x years
$$\eqalign{ & \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr & \Rightarrow 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr & \Rightarrow 26x + 78 = 23x + 138 \cr & \Rightarrow 3x = 60 \cr & \Rightarrow x = 20 \cr} $$
Present age of Suresh = 2x years
$$\eqalign{ & {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr & {\text{ = 40 years}} \cr} $$
Suresh's age = 2x years
$$\eqalign{ & \therefore \frac{{2x + 6}}{{x + 6}} = \frac{{23}}{{13}} \cr & \Rightarrow 13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \cr & \Rightarrow 26x + 78 = 23x + 138 \cr & \Rightarrow 3x = 60 \cr & \Rightarrow x = 20 \cr} $$
Present age of Suresh = 2x years
$$\eqalign{ & {\text{ = }}\left( {2 \times 20} \right){\text{ years }} \cr & {\text{ = 40 years}} \cr} $$