Question

The respective ages of A and B are in the ratio 3:4. Three years later their ages will be in the ratio 7:9. The present age of

B ​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given:-

• the respective ages of A and B are in the ratio 3:4,
• three years later their ages will be in the ratio 7:9.

To find :-

• The present age of B.

Solution :-

Let x be the common multiple of the ratio, 3:4, then,

Age of A = 3x years

Age of B = 4x years

Ratio = 3x : 4x

As per the question,

3 years later the ratio of their ages will become 7:9

Age of A = 3x + 3

Age of B = 4x + 3

Ratio = 3x + 3 : 4x + 3 = 7 : 9

$\bf\large\frac{3x + 3}{4x + 3}$ = $\bf\large\frac{7}{9}$

Cross multiplying,

9(3x + 3) = 7 (4x + 3)

27x + 27 = 28x + 21

27 - 21 = 28x - 27x

6 = x

x = 6.

Value of common multiple, x = 6

Substitute the value of x in,

• Age of person A = 3x
• Age of person B = 4x

$\bf{\large{\underline{\boxed{\rm{\red{Age\:of\:person\:A = 3x = 3 × 6 = 18 years.}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\green{Age\:of\:person\:B = 4x = 4 × 6 = 24 years.}}}}}}$

Present age of person B = 24 years.

$\bf{\huge{\underline{\boxed{\rm{\pink{Verification:}}}}}}$

For first case :-

• the respective ages of A and B are in the ratio 3:4,

Present age of person A = 18 years

Present age of person B = 24 years

$\bf\large\frac{18}{24}$ = $\bf\large\frac{3}{4}$

On dividing the LHS by 6,

$\bf\large\frac{3}{4}$ = $\bf\large\frac{3}{4}$

LHS = RHS.

For second case :-

• three years later their ages will be in the ratio 7:9

$\bf{\large{\underline{\boxed{\rm{\blue{3\: years\: later\: age\: of\: person\: A = 3x + 3 = 3\: × 6 + 3 = 18+ 3 = 21\:years }}}}}}$

$\bf{\large{\underline{\boxed{\rm{\red{3\: years\:later\:Age\:of\:person\:B\: = 4x + 3 = 4 ×6 + 3 = 24 + 3 = 27 years}}}}}}$

Age of person A: Age of person B,21: 27

$\bf\large\frac{21}{27}$ = $\bf\large\frac{7}{9}$

On dividing the LHS by 3,

$\bf\large\frac{7}{9}$ = $\bf\large\frac{7}{9}$

LHS = RHS.

Hence, we conclude our answer to be right.