Question

Present ages of Anu and Raj are in the ratio of 4:5. Eight years from now the ratio of there ages will be 5:6. Find there present ages.​

Answer 1

Answer:

Let the present age of Anu is 4x. Then, the present age of Raj will be 5x. so, Present age of Anu is 32 years and present age of Raj is 40 years.

Step-by-step explanation:

Let ages of them be x

According to question,

4x+8+5x+8=5x+6x

9x+16=11x

11x–9x=16

2x=16

x=16/2

x=8

Therefore,

Present age of anu=4x

4x8

32 years

Present age of raj=5x

5x8

40years

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Answer 2

$\sf Present\:Age \:\:\xrightarrow{After\:8\:Years} \:\:Future\:Age\\{\sf Anu : Raj \qquad\qquad\qquad\:\:\: Anu : Raj} \\{\:\:\:\sf 4 \::\:5 \qquad \qquad \qquad\qquad\:\: 5 : 6}$

Let the present age of Anu be 4x and Raj be 5x respectively.

$\rule{130}2$

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

$\begin{lgathered}:\implies\sf \dfrac{Anu+8}{Raj+8}=\dfrac{5}{6}\\\\\\:\implies\sf \dfrac{4x + 8}{5x + 8} = \dfrac{5}{6} \\\\\\:\implies\sf (4x + 8) \times 6= 5 \times (5x + 8)\\\\\\:\implies\sf 24x + 48 = 25x + 40\\\\\\:\implies\sf 48 - 40 = 25x - 24x\\\\\\:\implies\:\underline{\boxed{\sf x = 8\:years}}\:\: \bigstar\end{lgathered}$

$\rule{130}2$

☯ $\underline{\boldsymbol{Present\: Age\:of\: Anu\:\&\:Raj:}}$

$\begin{lgathered}\bullet\:\:\textsf{Anu = 4x = 4(8) = \textbf{32 years}}.\\\bullet\:\:\textsf{Raj = 5x = 5(8) = \textbf{40 years}}.\end{lgathered}$

$\rule{130}2$