Question

Present ages of Sameer and Anand are in ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand’s present age in years?
$
  {\text{A}}{\text{. 24 years}} \\
  {\text{B}}{\text{. 27 years}} \\
  {\text{C}}{\text{. 40 years}} \\
  {\text{D}}{\text{. 30 years}} \\
$

Answer 1

Hint: Here, we will proceed by eliminating the ratios and assuming the present ages as 5x and 4x. Similarly, the new ages are 11y and 9y. Then we will form two linear equations in two variables using the conditions given above. Solving these equations will help us reach the answer.

Complete Step-by-Step solution:
We have been given that the present ages of Sameer and Anand are in ratio of 5:4 respectively.
So let the present age of Sameer be 5x, then the present age of Anand will be 4x.
We are also given that their ages after 3 years are in ratio will become in ratio 11:9.
So let the then age of Sameer be 11y, and the then age of Anand be 9y.
Now, as the ages 11y and 9y are after three years, so,
$ \Rightarrow 5x + 3 = 11y$……………. Equation (1)
 and $4x + 3 = 9y$ ……………. Equation (2)
Subtracting Equation (2) from Equation (1), we get,
$x = 2y$ ………………Equation (3)
Using the value of x from Equation (3) in Equation (1), we get,
$5\left( {2y} \right) + 3 = 11y$
$ \Rightarrow y = 3$
And $x = 6$
Now, Anand’s present age is 4x, which is equal to 24 years.
Hence the option A is correct.

Note: Whenever we face such types of problems the main point to remember is that we need to have a good grasp over linear Equations in two variables. In this particular problem, students usually don’t take different variables for both the ratios and assume a single variable; this is completely wrong as both the ratios are not in proportion whereas there is a linear relation between its values. We could have also used matrices to solve this question but it is usually harder to solve matrices.