Question

Solve this plzzzz.....!

Answer 1

QuêSTion :

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

Present age of Anu = 4x = 4(8) = 32

Present age of Raj = 5x = 5(8) = 40

Step-by-step-explaination

Given :

• Present age ratio = 4:5

• Eight years later , ratio will be in ratio : 5:6

To Find :

• Present ages = ??

Procedure :

Present ages are in ratio 4 and 5.

So, let's assume the present age age to be 4x and 5x.

8 years later , age will be :-

$\sf \implies \: 4x + 8 \: and \: 5x + 8$

The question says that 8 years hence ratio will be 5:6.

So, age after 8 years be 5x and 6x.

Now , according to the given conditions. We get ,

$\sf \implies \: 4x + 8 + 5x + 8 = 5x + 6x$

$\sf \implies \: 4x + 5x + 8 + 8 = 5x + 6x$

$\sf \implies \: 9x + 16 = 5x + 6x$

Transferring the constant to RHS and variable based expression to RHS.

$\sf \implies \: 9x - 5x - 6x = - 16$

$\sf \implies \: - 2x = - 16$

Negatives will get cancelled.

$\sf \implies \: 2x = 16$

$\sf \implies \: x = \dfrac{16}{2}$

$\sf \implies \: x = 8$

Present age of Anu = 4x = 4(8) = 32

Present age of Raj = 5x = 5(8) = 40

Answer :

• Present Anu's age = 32 years.

• Present Raj's = 40 years.

Answer 2

Step-by-step explanation:

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

⠀

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

$\rule{130}2$

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

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

$\rule{130}2$

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

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

$\rule{130}2$