Question

The ages of Hari and Harry are in the ratio 2:5. 5 years from now the ratio of their ages wil be 3:5 . The present age of Hari is *​

Answer 1

Answer:

Given :-

• The ages of Hari and Harry are in the ratio of 2 : 5.
• 5 years from now the ratio of their ages will be 3 : 5.

To Find :-

• What is present age of Hari.

Solution :-

Let,

➲ Present age of Hari be 2x years

➲ Present age of Harry will be 5x years

❒ Five years from now their ages will be :

➭ Age of Hari = 2x + 5

➭ Age of Harry = 5x + 5

According to the question,

$\implies \sf (2x + 5) : (5x + 5) =\: 3 : 5$

$\implies \sf \dfrac{2x + 5}{5x + 5} =\: \dfrac{3}{5}$

By doing cross multiplication we get,

$\implies \sf 3(5x + 5) =\: 5(2x + 5)$

$\implies \sf 15x + 15 =\: 10x + 25$

$\implies \sf 15x - 10x =\: 25 - 15$

$\implies \sf 5x =\: 10$

$\implies \sf x =\: \dfrac{\cancel{10}}{\cancel{5}}$

$\implies \sf\bold{\purple{x =\: 2}}$

Hence, their present ages are :

◘ Present Age Of Hari :

↦ Present Age Of Hari = 2x years

↦ Present Age Of Hari = (2 × 2) years

➠ Present Age Of Hari = 4 years

◘ Present Age Of Harry :

↦ Present Age Of Harry = 5x years

↦ Present Age Of Harry = (5 × 2) years

➠ Present Age Of Harry = 10 years

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Hari\: is\: 4\: years\: .}}}}$

Answer 2

${ \textbf{\textsf{ \underline{ \underline{{Given \: :}{\quad}}}}}}$

• The ages of Hari and Harry are in the ratio 2:5. Five years from now the ratio of their ages wil be 3:5.

${ \textbf{\textsf{ \underline{ \underline{{To Find \: :}{\quad}}}}}}$

• Present age of Hari.

${ \textbf{\textsf{ \underline{ \underline{{Solution \: :}{\quad}}}}}}$

• Let's assume the present age of Hari as 2y.

• Let's assume the present age of Harry as 5y.

$\bigstar \: \: { \underline{ \boldsymbol{ \underline{After \: Five \: years \: their \: ages \: will \: be:}}}}$

➬ Hari's age = 2y + 5

➬ Harry's age = 5y + 5

${\textbf {\textsf{Now, According to the Question \: :}}}$

$\\ \tt⇢(2y+5):(5y+5)=3:5 \\ \\ \\ ⇢ \tt \: \dfrac{2y + 5}{5y + 5} =\: \dfrac{3}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

By doing cross multiplication we get,

$⇢ \: \tt 3(5y+ 5) =\: 5(2y + 5)\\ \\ \\ ⇢ \tt15y + 15 = 10y+ 25 \: \: \\ \\ \\ ⇢ \tt15y - 10y = 25 - 15 \\ \\ \\ ⇢ \: \: \tt5y = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt ⇢ \: \: y = \frac{10}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢ \: \: \: \: \: { \boxed{\pink{ \pmb{ \mathfrak{y = 2}}}}}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore, their present ages are :

$\begin{gathered} \\ ⇢ { \textbf{ \textsf{Present age of Hari}}} = \tt 2y \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: 2 \times 2\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: \pmb{\mathfrak{4 \: years}}\\ \\ \end{gathered}$

$\begin{gathered} \\ ⇢ { \textbf{ \textsf{Present age of Hari}}} = \tt 5y \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: 5 \times 2\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: \pmb{\mathfrak{10 \: years}}\\ \\ \end{gathered}$

Hence, The Present age of Hari and Harry are 4 years and 10 years.