Question

The ages of A and B are in the ratio 8:3. Six year hence their ages will be in the ratio 4:9 the percent ages .​

Answer 1

Correct Question :

The ages of A and B are in the ratio 8:3. Six year hence their ages will be in the ratio 9:4 the present ages .

Given :

• The ages of A and B are in the ratio 8:3 .
• After 6 years their ages will be in the ratio 9:4 .

To Find :

• Present Ages of A and B .

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:A\:be=8x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:B\:be=3x}$

After 6 years :

$\longmapsto\tt{Age\:of\:A=8x+6}$

$\longmapsto\tt{Age\:of\:B=3x+6}$

A.T.Q :

$\longmapsto\tt{\dfrac{8x+6}{3x+6}=\dfrac{9}{4}}$

$\longmapsto\tt{4(8x+6)=9(3x+6)}$

$\longmapsto\tt{32x+24=27x+54}$

$\longmapsto\tt{32x-27x=54-24}$

$\longmapsto\tt{5x=30}$

$\longmapsto\tt{x=\cancel\dfrac{30}{5}}$

$\longmapsto\tt\bf{x=6}$

Value of x is 6 ..

Therefore :

$\longmapsto\tt{Present\:Age\:of\:A=8(6)}$

$\longmapsto\tt\bf{48\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:B=3(6)}$

$\longmapsto\tt\bf{18\:yrs}$

Answer 2

$\huge \purple A \purple N \purple s \purple W \purple e \purple \R : -$

Let A'sage be 8x and B's age be 3x

According to question, we have,

8x + 6 / 3x + 6 = 9/4

=>32x+24=27x+54

=>5x=30

=>x=6

A's age =8×6=48

B's age =3×6=18

A+B

=48+18

=66 years