Question

the present ages of a and b ate the ratio is 9:2 ten years age there ages were 3:4. what are their present ages ?

Answer 1

Solutions :-

We have,

Present ages of A and B are in the ratio 9:2

After 10 years, the  ratio will changed,

the ratio of their ages will be 3:4

Now,

We have to find the present age of A and B

Let the age of A and B be 9x and 2x respectively.

Find the value of x :-

A/q

=> (9x + 10)/(2x + 10) = 3/4

=>  4(9x + 10) = 3(2x + 10)

=> 36x + 40 = 6x + 30

=> 36x - 6x = 40 - 30

=> 30x = 10

=> x = 10/30 = 1/3

Therefore, A age = 9x = 9×1/3 = 3

B age = 2x = 2 × 1/3 = 2/3

Answer : Age of A = 3 years

Age of B = 2/3 years

Answer 2

Solutions :-

Given :

Present ages of A and B are in the ratio 9:2

After 10 years, the ratio of their ages will be 3:4

Let the present age of A be 9x
And B be 2x

A/q

$= > \frac{9x + 10}{2x + 10} = \frac{3}{4} \\ \\ = > 4(9x + 10) = 3(2x + 10) \\ \\ = > 36x + 40 = 6x + 30 \\ \\ = > 36x - 6x = 40 - 30 \\ \\ = > 6x = \frac{10}{30} \\ \\ = > x = \frac{1}{3}$

Now,
Age of A = 9x = 9×1/3 = 3
Age of B = 2x = 2×1/3 = 2/3

Hence,
The present age of A is 3 years and B is 2/3 years or 8 months