Question

The ratio of the present ages of Jai and Amy is 8:5. If their ages after 6 years would be in the ratio 11:8, find their present ages.​

Answer 1

Given :

• The ratio of the present ages of Jai and Amy is 8:5. If their ages after 6 years would be in the ratio 11:8.

To Find :

• Present ages

Solution :

✦Let the Jai's age be 8x then Amy's age be 5x

• After 6 years
• Jai's age = (8x + 6)
• Amy's age = (5x + 6)

✪ According to the given condition

➨ (8x + 6)/(5x + 6) = 11/8

➨ 8(8x + 6) = 11(5x + 6)

➨ 64x + 48 = 55x + 66

➨ 64x - 55x = 66 - 48

➨ 9x = 18

➨ x = 18/9

➨ x = 2

Hence,

• Present age of Jai = 8x = 16years
• Present age of Amy = 5x = 10years

Answer 2

⚽ Solution:

$\sf Present\:Age \:\:\xrightarrow{After\:6\:Years} \:\:Future\:Age\\{\sf Jai : Amy \qquad\qquad\qquad\: \:\:\:Jai: Amy} \\{\:\:\sf 8 \::\:5 \qquad \qquad\qquad \qquad 11 : 8}$

Let the present age of Jai be 8x and Amy be 5x respectively.

$\rule{130}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\begin{lgathered}:\implies\sf \dfrac{Jai+6}{Amy+6}=\dfrac{11}{8}\\\\\\:\implies\sf \dfrac{8x + 6}{5x + 6} = \dfrac{11}{8} \\\\\\:\implies\sf (8x + 6) \times 8 = 11 \times (5x + 6)\\\\\\:\implies\sf 64x + 48 = 55x + 66\\\\\\:\implies\sf 64x - 55x = 66 - 48\\\\\\:\implies\:\underline{\boxed{\sf x = 2\:years}}\: \bigstar\end{lgathered}$

$\rule{130}2$

☯ $\underline{\boldsymbol{Present\: Age\:of\: Jai\:\&\:Amy:}}$

$\begin{lgathered}\bullet\:\:\textsf{Jai = 8x = 8(2) = \textbf{16 years}}\\\bullet\:\:\textsf{Amy = 5x = 5(2) = \textbf{10 years}}\end{lgathered}$

$\rule{130}2$