Question

the present ages of ajay and vijay are in ratio 4:5. Four years from now their ages will be in ratio 5:6. Find their present age.​

Answer 1

❍ The Given ratio of present ages of Ajay and Vijay is 4: 5. So, Let's say the present ages of Ajay and Vijay are 4x and 5x respectively.

☆ Four years from now their ages —

Ajay's age after four years = (4x + 4)

Vijay's age after four years = (5x + 4)

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$\sf\small\underline\red{According \: to \: the \: question:-}$

Four years from now their ages (Ajay's age and Vijay's age) will be in the ratio of 5: 6.

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Therefore,

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$\begin{gathered}:\implies\sf \bigg(\dfrac{4x + 4}{5x + 4} \bigg) = \bigg(\dfrac{5}{6}\bigg) \\\\\\:\implies\sf 6(4x + 4) = 5(5x + 4) \\\\\\:\implies\sf 24x + 24 = 25x + 20\\\\\\:\implies\sf 24x - 25x = 20 - 24 \\\\\\:\implies\sf -x = -4\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 4}}}}}\;\bigstar\end{gathered}$

Hence,

Ajay's present age = 4x = 4(4) = 16 years

Vijay's present age = 5x = 5(4) = 20 years

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$\therefore{\underline{\sf{Hence, their\: present\;ages\:are\;\bf{16\; years\;\&\;20\:years }.}}}∴$

$\rule{250px}{.3ex}$

V E R I F I C A T I O N :

It is given as, Four years from now their ages (Ajay's age and Vijay's age) will be in the ratio of 5: 6. So, let's verify their ages :

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$\begin{gathered}\dashrightarrow\sf \dfrac{4x + 4}{5x + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{4(4) + 4}{5(4) + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{16 + 4}{20 + 4} = \dfrac{5}{6}\\\\\\\dashrightarrow\sf \cancel\dfrac{20}{24} = \dfrac{5}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{\dfrac{5}{6} = \dfrac{5}{6}}}}\end{gathered}$

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

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Answer 2

Answer:

❍ The Given ratio of present ages of Ajay and Vijay is 4: 5. So, Let's say the present ages of Ajay and Vijay are 4x and 5x respectively.

☆ Four years from now their ages —

Ajay's age after four years = (4x + 4)

Vijay's age after four years = (5x + 4)

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀

⠀⠀⠀⠀ ㅤㅤㅤㅤ

$\sf\small\underline\red{According \: to \: the \: question:-}$

Four years from now their ages (Ajay's age and Vijay's age) will be in the ratio of 5: 6.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore,

⠀

$\begin{gathered}:\implies\sf \bigg(\dfrac{4x + 4}{5x + 4} \bigg) = \bigg(\dfrac{5}{6}\bigg) \\\\\\:\implies\sf 6(4x + 4) = 5(5x + 4) \\\\\\:\implies\sf 24x + 24 = 25x + 20\\\\\\:\implies\sf 24x - 25x = 20 - 24 \\\\\\:\implies\sf -x = -4\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 4}}}}}\;\bigstar\end{gathered}$

Hence,

Ajay's present age = 4x = 4(4) = 16 years

Vijay's present age = 5x = 5(4) = 20 years

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$\therefore{\underline{\sf{Hence, their\: present\;ages\:are\;\bf{16\; years\;\&\;20\:years }.}}}∴$

$\rule{250px}{.3ex}$

V E R I F I C A T I O N :

It is given as, Four years from now their ages (Ajay's age and Vijay's age) will be in the ratio of 5: 6. So, let's verify their ages :

⠀

$\begin{gathered}\dashrightarrow\sf \dfrac{4x + 4}{5x + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{4(4) + 4}{5(4) + 4} = \dfrac{5}{6} \\\\\\\dashrightarrow\sf \dfrac{16 + 4}{20 + 4} = \dfrac{5}{6}\\\\\\\dashrightarrow\sf \cancel\dfrac{20}{24} = \dfrac{5}{6} \\\\\\\dashrightarrow\underline{\boxed{\frak{\dfrac{5}{6} = \dfrac{5}{6}}}}\end{gathered}$

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

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