Question

Nine years ago, age of two brothers were inthe ratio 2:3. Six years later their ages will be in ratio 7:8 . find their present age

Answer 1

Hope u understood well.........

Answer 2

Answer:

The present ages are 15 years and 18 years.

Explanation:

Let the present ages be X and Y years.

according to the question,

using the first statement,

we get

Step 1:

(X-9):(Y-9)= 2:3

3(X-9)=2(Y-9)

3X-27=2Y-18

3X-2Y=9............(A)

and

Step 2:

(X+6):(Y+6)=7:8

8(X+6)=7(Y+6)

8X+48=7Y+42

8X-7Y=-6..........(B)

SOLVING EQUATIONS (A) AND (B)

WE GET,

multiply equation (a) by 7 and (b) by 2,

Step 3:

21X-14Y=63...........(C)

16X-14Y=-12...........(D)

now solving equation (C) and (D) we get,

5X=75

X=15

Step 4:

put the value of X in equation (A), WE GET THE VALUE OF Y

Y= 18

Hence, the present ages are 15 years and 18 years.

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