Question

The age of A is 5 yr more than of B.5 yr ago, the ratio of their ages was 3:2. Find their present ages.

Answer 1

I think this is the answer but I am not sure please check.

Answer 2

Let the present age of A and B be a and b respectively.

Condition 1:

a = b + 5 ----- Eq 1

Condition 2:

$\frac{a - 5}{b - 5} = \frac{3}{2}$

2a - 10 = 3b - 15

i.e. 2a - 3b - 10 + 15 = 0

i.e. 2a - 3b + 5 = 0 ------ Eq 2

Substituting a=b+5 in Eq 2,

2(b + 5) - 3b + 5 = 0

i.e. 2b + 10 - 3b + 5 = 0

i.e. -b + 15 = 0

i.e. b = 15

Substituting b=15 in Eq 1,

a = b + 5 = 15 + 5 = 20

a = 20

The present age of A is 20 years.

The present age of B is 15 years.

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