Question

Ten years ago sameer was half of rahul's age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages?

Answer 1

Let Sameer's present age be x. Then his age 10 years ago was x-10. Because Rahul was twice as old as Sameer 10 years ago, his age was 2x-20 10 years ago, which means that his age now is 2x-10.

So, the ratio between Sameer's present age(x) and Rahul's(2x-10) is $\frac{3}{4}$. This means that $\frac{x}{2x-10} =\frac{3}{4}$, from which we get that $4x=6x-30$. From there $2x=30$ and thus $x=15$.

As Sameer's age is x, and Rahul's is 2x-10, we get that Sameer's present age is 15, and Rahul's is 20. So, the total of their present ages is 35.

Answer 2

Given:

Ten years ago Sameer was half of Rahul's age. If the ratio of their present ages is 3:4.

To find:

The total of present ages of Sameer and Rahul.

Solution:

As given,

The ratio of the present age of Sameer and Rahul is 3:4.

Let the highest common factor between the present ages of Sameer and Rahul be x.

So,

the present age of Sameer = 3x

the present age of Rahul = 4x

Before 10 years,

the age of Sameer = 3x - 10

the age of Rahul = 4x - 10

Now,

according to the question,

Ten years ago,

Sameer's age = half of Rahul's age.

$3x - 10 = \frac{1}{2} (4x - 10)$

On solving, we get

$6x - 20 = 4x - 10$

$2x = 10$

$x = 5 \:$

On putting the value of x in

Sameer's present age

$= 3(5)$

$= 15 \: years$

Rahul's present age

$= 4(5)$

$= 20 \: years$

Sum of the present age of Sameer and Rahul

$= 20 + 15 = 35 \: years$

Hence, the sum of the present ages of Sameer and Rahul is 35 years.