Question

The ratio of the present ages of A and B is 5:6. The ratio of their ages five years before was 45 Find their present
ages.​

Answer 1

Given:-

• Ratio of Present Age = 5:6

• Ratio of ages five years before = 4:5

To Find:-

• The Present age of A & B.

Solution:-

Let the age of 'A' be 5x....................(i)

and, the age of 'B' be 6x.................(ii)

Now, Age of 'A' & 'B' five years before

(5x-5)/(6x-5) = 4/5 (here ratio is written in fraction)

→ (5x-5)/(6x-5) = 4/5

Cross multiplication

→ 5(5x-5) = 4(6x-5)

→ 25x-25 = 24x - 20

→ 25x-24x = -20+25

→ x = 5

Now, Substitute the value of x in equation (i) & (ii) we get

→ 5x = 5×5 = 25years

→ 6x = 6×5 = 30years

∴The present age of 'A' is 25 years.

And, the present age of 'B' is 30 years.

Answer 2

Given:-

• ratio between the ages of A and B = 5:6
• ratio between their ages 5 years ago = 4:5

To find:-

• their present ages.

Supposition:-

let the age of A be 5x

let the age of B be 6x.

according to the question:-

:$\implies$ $\sf\dfrac{5x-5}{6x-5}$ = $\sf\dfrac{4}{5}$

:$\implies$ ${\sf 5(5x-5)}$ = ${\sf 4(6x-5)}$

:$\implies$ ${\sf 25x-25}$ = ${\sf 24x-20}$

:$\implies$ ${\sf x}$ = ${\sf 5}$

hence, the present age of A is 5(5) = 25 years.

and present age of B is 6(5) = 30 years.