Question

The ratio of the present ages of two brothers is 1 : 2 and 5 year before their ages were in the ratio of 1:3. Then find the ratio of their ages after 5 years

Answer 1

Answer:

A : B = 3 : 5

Step-by-step explanation:

Let A and B are two brothers.

Given that- ratio of the present ages of A and B is 1 : 2.

Let age of A = x years

Age of B = 2x years

Before five years-

Age of A = (x - 5) years

Age of B = (2x - 5) years

Ratio = 1 : 3

(x - 5) : (2x - 5) = 1 : 3

$\dfrac{x - 5}{2x - 5} = \dfrac{1}{3}$

By crossing multiplication-

3(x - 5) = 1(2x - 5)

3x - 15 = 2x - 5

3x - 2x = -5 + 15

x = 10

Present age of A = 10 years

Present age of B = 2x

                            = 2 × 10

Present Age of B = 20 years

After five years-

Age of A = 10 + 5

Age of A = 15 years

Age of B = 20 + 5

Age of B = 25 years

Ratio of ages of A and B-

$\dfrac{A}{B} = \dfrac{15}{25}$

                         = $\dfrac{3 \times 5}{5 \times 5}$

A : B = 3 : 5