Question

12. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years? [SSC) (a) 1:1 (b) 2:3 (c) 3:5 (d) 5 6 will be twice the age of his son. ​

Answer 1

❍ Let's Consider that, the ages of the two brothers are x years and 2x years respectively.

— Five years back :

• First brother's age = (x – 5)
• Second brother's age = (2x – 5)

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

• It is given that five years back, the ratio of their ages was 1 : 3. Therefore,

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$:\implies\sf{\bigg\{\dfrac{x-5}{2x-5}\bigg\}=\bigg\{\dfrac{1}{3}\bigg\}}\\\\\\:\implies\sf{3\Big\{x-5}\Big\}=\Big\{2x-5\Big\}\\\\\\:\implies\sf{3x-15=2x-5}\\\\\\:\implies\sf{3x-2x=-5+15}\\\\\\:\implies\underline{\boxed{\frak{\pmb{x=10}}}}\;\bigstar$

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Hence,

• First brother's age = x = 10 years
• Second brother's age = 2x = 2(10) = 20 years

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★ Ratio of their ages after five years :

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$\twoheadrightarrow\;\sf{Ratio=\bigg\{\dfrac{10+5}{20+5}\bigg\}}$

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$\twoheadrightarrow\;\sf{Ratio=\bigg\{\dfrac{15}{25}\bigg\}}$

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$\twoheadrightarrow\;\underline{\boxed{\sf{\pmb{\pink{Ratio\;=\;3:5}}}}}\;\bigstar$

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$\therefore\;{\underline{\textsf{Hence,\;the\;required\;ratio\;of\;their\;ages\;is\;{\textbf{3\;:\;5}},\;option\;(c).}}}$⠀⠀⠀

Answer 2

$\large\pmb{\frak{\underline{Answer~:}}}$

• Option c)
• 3:5 is correct Option ✓

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Given : The ratio of present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3.

To Find : Find the ratio of their ages after 5 years ?

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Solution : let's say that the present ages of the two brothers be x & 2x.

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• Five years back, the ratio of their ages (both brother's ages) was 1 : 3.

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Therefore,

• Five years ago their ages —

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◗Younger brother = (x – 5)

◗Elder brother = (2x – 5)

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$\pmb{\sf{\underline{According ~to~ the~ Given~ Question~:}}}$

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$\qquad{\sf:\implies{\bigg\{\dfrac{x~-~5}{2x~-~5}\bigg\}~=~\bigg\{\dfrac{1}{3}\bigg\}}}$

$\qquad{\sf:\implies{3\bigg\{x~-~5\bigg\}~=~\bigg\{2x~-~5\bigg\}}}$

$\qquad{\sf:\implies{3x~-~15~=~2x~-~5}}$

$\qquad{\sf:\implies{3x~-~2x~=~- 5~+~15}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x~=~10}}}}}}$★

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Henceforth,

• Present ages of both brother are, x = 10 years
• 2x = 2(10) = 20 years

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◗Present ages of two brothers are 10 years & 20 years.

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R A T I O :

• After five years the ratio their ages will be –

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$\qquad{\sf:\implies{\dfrac{10~+~5}{20~+~5}}}$

$\qquad{\sf:\implies{\cancel\dfrac{15}{25}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{\dfrac{\pmb{3}}{\pmb{5}}}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{The~ratio~of~their ~ages~ after~ 5 ~years~will~be~\bf{\underline{\pmb{3 : 5}}}}}$