Question

the ages of sourav and sachin are in the ratio 3:2. Twelve years from now the ratio of their ages will be 6:5, find their ages??​

Answer 1

❍ Let's consider that, the age of Sourav be 3x years and age of Sachin be 2x years.

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• After twelve years, the ratio of their ages will be 6:5.

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Therefore,

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$\begin{gathered}:\implies\sf{\dfrac{3x+12}{2x+12}=\dfrac{6}{5}}\\\\\\\\:\implies\sf{5(3x+12)=6(2x+12)}\\\\\\\\:\implies\sf{15x+60=12x+72}\\\\\\\\:\implies\sf{15x-12x=72-60}\\\\\\\\:\implies\sf{3x=12}\\\\\\\\:\implies\sf{x=\cancel{\dfrac{12}{3}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{x=4}}}}\;\bigstar\end{gathered}$

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Hence,

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• Sourav's age = 3x, 3(4) = 12 years
• Sachin's age = 2x, 2(4) = 8 years

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$\therefore\;{\underline{\sf{Hence,\;their\;ages\;are\;{\textsf{\textbf{12\;years}}}\;\&\;{\textsf{\textbf{8\;years}}}}.}}$⠀⠀⠀

Answer 2

Let the present age of the Sourav and sachin are 3x and 2x Respectively.

After Twelve years,

• Sourav's age be (3x + 12) years
• Sachin's age be (2x + 12) years

Finally, After twelve years from Now their ages ratio will be 6:5.

→ 5(3x + 12) = 6(2x + 12)

→ 15x + 60 = 12x + 72

→ 15x - 12x = 72 - 60

→ 3x = 12

→ x = 12/3

→ x = 4

Hence,

• Present age of Sourav = 12 years
• Present age of Sachin = 8 years