At present, the ratio of the age of Ram and Sanjay is 2:3, and after 5 years from now, its ratio will get changed to 6:7. What is Ram’s present age?

At present, the ratio of the age of Ram and Sanjay is 2:3, and after 5 years from now, its ratio will get changed to 6:7. What is Ram’s present age?

Let's assume the present age of Ram is 2x years and the present age of Sanjay is 3x years, where x is a common factor.

According to the given information, the ratio of their present ages is 2:3. So, we can set up the equation:

2x/3x = 2/3

Cross-multiplying, we get:

2(3x) = 3(2x)

6x = 6x

This equation shows that the ratio is consistent, so we can proceed to the next condition.

After 5 years from now, the ratio of their ages will be 6:7. Let's calculate their ages at that time:

Ram's age after 5 years: 2x + 5

Sanjay's age after 5 years: 3x + 5

According to the given information, the ratio of their ages after 5 years is 6:7. So, we can set up the equation:

(2x + 5)/(3x + 5) = 6/7

Cross-multiplying, we get:

7(2x + 5) = 6(3x + 5)

14x + 35 = 18x + 30

4x = 5

x = 5/4

Now that we know the value of x, we can find Ram's present age:

Ram's present age = 2x = 2(5/4) = 10/4 = 5/2 = 2.5 years

Therefore, Ram's present age is 2.5 years.