Question

THE AGE OF A AND B IN RATIO 8:3 .Six year hence.their age will be 9:4 FIND THE PRESENT AGE.


fast...

​

Answer 1

Answer:

• A = 48 years.
• B = 24 years.

Explanation:

Given age ratio of A and B is 8 : 3

After 6 years the age ratio becomes 9 : 4

Let's assume the age of,

• A = $\boldsymbol{8x}$
• B = $\boldsymbol{3x}$

Now,

After 6 years age of,

• A = $\boldsymbol{(8x + 6)}$ years.
• B = $\boldsymbol{(3x + 6)}$ years.

According to the question,

${ \implies \boldsymbol{(8x + 6) : (3x + 6) = 9 : 4}}$

$\implies \boldsymbol{ \dfrac{(8x + 6)}{(3x + 6)} = \dfrac{9}{4} }$

$\implies \boldsymbol{4(8x + 6) = 9(3x + 6)}$

$\implies \boldsymbol{32x + 24 = 27x + 54}$

$\implies \boldsymbol{32x - 27x = 54 - 24}$

$\implies \boldsymbol{5x = 30}$

$\implies \boldsymbol{x = \dfrac{30}{5} }$

$\implies \boldsymbol{x = 6} \:$

Hence,

The age of,

• A = $\boldsymbol{8x = 8(6) = 48 \: years. }$
• B = $\boldsymbol{3x = 3(8)= 24 \: years }$

Answer 2

$\huge \fbox{\sf{\underline{answer}}} \rightarrow$

$\large \frak \green {\pmb{ \underline{given : }}}$

• The age of A and B is in ratio 8 : 3
• After 6 year their age will be 9 : 4

$\:$

$\large \frak \green {\pmb{ \underline{to \: find : }}}$

• Find their present ages..?

$\:$

$\large \frak \green {\pmb{ \underline{solution : }}}$

$\sf{ let \: their \: present \: age \: be \: 8x \: and \: 3x.}$

$\sf{ \therefore \: After \: 6 \: years \: their \: age \: will \: be \: A = 8x + 6 \: and \: B = 3x + 6}$

$\sf{ \qquad : \implies \: \frac{8x + 6}{3x + 6} = \frac{9}{4} }$

$\sf{ \qquad : \implies \: 4(8x + 6) = 9(3x + 6)...by \: cross \: multipication}$

$\sf{ \qquad : \implies \: 32x + 24 = 27x + 54}$

$\sf{ \qquad : \implies \: 32x - 27x = 54 - 24}$

$\sf{ \qquad : \implies \: 5x = 30}$

$\sf{ \qquad : \implies \: x = \frac{30}{5} }$

$\sf{ \qquad : \implies \: x = 6}$

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

$\sf{present \: age \: of \: A = 8x = 8 \times 6 = 48}$

$\sf{ present \: age \: of \: B = 3x = 3 \times 6 = 18}$

$\qquad \: \: \: \: \: \: \: \: \: \frak \color{skyblue}{ \underline{Hope \: it \: helps \: you}}$