Question

The sum of the age of Ramesh and Kamal is 84 years. If 6 years ago the ratio of their ages is 5:7 respectively, find the present age of Kamal.

Answer 1

Hint: Let the age of Ramesh and Kamal six years ago be $5x$ and $7x$ respectively where $x$ is the common factor of the ratio . Form the equation using the given condition and solve it to find the value of $x$. Substitute the value of $x$ in the expression for the present age of Kamal, that is, $7x + 6$.

Complete step by step answer:
We are given the ratio of the ages 6 years ago of Ramesh and Kamal as 5:7
First of all, let the age six years ago of Ramesh be $5x$ and the age of Kamal six years ago be $7x$.
The present age of Ramesh will be $5x + 6$ and the present age of Kamal age be $7x + 6$.
We are given that the sum of the present ages of Ramesh and Kamal is 84 years.
Therefore, we can write it as,
$5x + 6 + 7x + 6 = 84$
On combining the like terms, we get,
$
  12x + 12 = 84 \\
  12x = 72 \\
$
Divide the equation throughout by 12.
$x = 6$
The present age of Kamal is given by $7x + 6$.
On substituting, $x = 6$, we get,
$7\left( 6 \right) + 6 = 42 + 6 = 48{\text{ years}}$
Hence, the present age of Kamal is 48 years.

Note: Ratio is a method of relating objects. If the ratio is given as $a:b$, then there exists a common factor of $a$ and $b$. Ratios do not have any units but the objects of which ratio is calculated can have a unit. Formulate the equation carefully according to the relation given in the question.