Question

10 years ago A was 1/3rd of Q's age. If the ratio of the present ages of A and Q is 4:7,what is the total sum of their ages after 5 years?

Answer 1

Answer:

Let the present age of A = x

let the present age of Q = y

Ten years ago, their ages were x-10 and y-10

We are given that (x-10) = 1/3*(y-10) ... Eqn 1 [A was 1/3rd of Q's age, ten years ago]

We are also given that the ratio of prsent ages of A and Q is 4:7, which means that x/y = 4/7 or 7x = 4y or x = 4y/7

Substituting for x in Eqn 1 and simplifying, we get:

12y/7 - 30 = y - 10

12y/7 - y = 20

5y/7 = 20

y = 28

Now, x = 4y/7 = 4*28/7 = 16

Present age of A is 16 and present age of Q is 28

(Verify: Ten years ago, A's age was 6 and Q's age was 18. Thus, A's age then was 1/3rd of Q's age then.)

After five years, A's age will be 21 and Q's age will be 33. The sum of their ages will be 21 + 33 = 54

Step-by-step explanation: