Question

Raj and Deepak are cousins. Seven times the difference between the ages of Deepak and Raj is the sum of their ages. Ratio of Deepak's age after 12 years and Raj's present age is 5:3. Find Raj's present
age.
24 years
30 years
36 years
25 years​

Answer 1

Answer:

The answer to your question is 36 years

Answer 2

Given:

The ratio of Deepak's age after 12 years and Raj's present age=5:3

To find:

Raj's present age

Solution:

Raj's present age is 36 years.

We can find the age by taking the given steps-

Let us assume that the present age of Raj and Deepak is X and Y.

We know that 7 times the difference between their ages is equal to the sum of their ages.

Using the information, we get

The difference between the ages of Deepak and Raj=Y-X

The sum of their ages=X+Y

So, 7×(Y-X)=X+Y

7Y-7X=X+Y

7Y-Y=7X+X

6Y=8X

X=6Y/8

X=3Y/4 (1)

Now, we are given that the ratio of Deepak's age after 12 years and Raj's present age is 5:3.

Deepak's age after 12 years=Present age+12

=Y+12

So, (Y+12): X=5:3

Y+12/X=5/3

3(Y+12)=5X

3Y+36=5X

From (1),

3Y+36=5(3Y/4)

3Y+36=15Y/4

36=15Y/4 -3Y

36=(15Y-12Y)/4

36×4=3Y

144=3Y

144/3=Y

48 years=Y

Using the value of Y,

X=3Y/4

X=3(48)/4

X=3×12

X=36 years

Therefore, Raj's present age is 36 years.