MathematicsThe ratio of the ages of A and B ten years before was 3:5. The ratio of their present ages is 2:3. Their ages are respectively,

The ratio of the ages of A and B ten years before was $3 : 5$ . The ratio of their present ages is $2 : 3$ . Their ages are respectively,

Given, the ratio of the ages of A and B ten years before was

3 : 5

.
Also, the ratio of their present ages is

2 : 3

.
Let the present ages of

A

and

B

are

x

years and

y

years respectively.
According to the given condition,
⇒

\frac{x - 10}{y - 10} = \frac{3}{5}

..... (1)
⇒

5 x - 50 = 3 y - 30

......(2)
Also,

\frac{x}{y} = \frac{2}{3}

⇒

3 x = 2 y

⇒

y = \frac{3 x}{2}

Putting the value of y in (1) we get,
⇒

5 x - 50 =

\frac{9 x}{2} - 30

⇒

10 x - 100 = 9 x - 60

⇒

x = 40

⇒

y = \frac{3 \times 40}{2}

⇒

y = 60

Hence, the correct option is 3.

JEE