Question

The present age of Suresh is twice his daughter's. Six years hence the ratio between the age of Suresh and his daughter will be 23:13. What is the present age of Suresh?
1) 40 years
2) 36 years
3) 46 years
4) Cannot be determined

Answer 1

Hint: First of all, we will write the expressions for the given statement by letting the age of Suresh’s daughter be $x$. We will express the equations in the form of a ratio. Then, we need to cross multiply and solve for the value of $x$. Finally, we need to substitute the value of $x$ in the expression for the age of Suresh.

Complete step-by-step answer:

We will begin by letting the present age of Suresh’s daughter be $x$.
Since, the age of Suresh is twice the age of his daughter, Suresh’s present age can be written as $2x$.
Now, we need to form the equation according to the given condition.
Six years means age after 6 years.
Hence, Suresh’s daughter will be $x + 6$ and Suresh’s age will be $2x + 6$.
We are given that the ratio of their ages will be 23:13, which can be represented as,
$\dfrac{{2x + 6}}{{x + 6}} = \dfrac{{23}}{{13}}$
We will cross-multiply the above expression to form an equation in $x$.
$
  13\left( {2x + 6} \right) = 23\left( {x + 6} \right) \\
  26x + 78 = 23x + 138 \\
  3x = 60 \\
  x = 20 \\
 $
Hence, the present age of daughter is 20 years and present age of father is $2 \times 2 = 40{\text{ years}}$
Therefore, option A is correct.

Note: Many students make mistakes while writing the ratio as $\dfrac{{x + 6}}{{2x + 6}} = \dfrac{{23}}{{13}}$, which is incorrect. The order in which the ratio is written is important in solving these types of questions. In the last step, find the father’s age after substituting the value of his daughter’s age.