Question

six years ago the ratio of Ages of Karan and Arjun was 6:5,
4 years from now the ratio of their ages will be 11:10 .

find their present ages
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Answer 1

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▪Given :-

• 6 years ago the ratio of Ages of Karan and Arjun was 6:5,
• 4 years from now the ratio of their ages will be 11:10 .

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▪To Find :-

Present Ages of Karan And Arjun

▪Solution :-

Let,

• Present age of Karan be = x years
• Present age of Arjun be = y years

《 6 years Ago 》

• Age of Karan = (x - 6) years

• Age of Arjun = (y - 6) years

According to the Given Condition :

$\sf \dfrac{x - 6}{y - 6} = \frac{6}{5} \\ \\ \sf5(x - 6) = 6(y - 6) \\ \\ \sf5x - 30 = 6y - 36 \\ \\ \bf \large 5x - 6y = - 6 \: \: \: \: .\: . \: . \: (i)$

《 4 Years Hence 》

• Age of Karan = (x + 4) years

• Age of Karan = (x + 4) years

According to the Given Condition :

$\sf \dfrac{ x+ 4}{y + 4} = \frac{11}{10} \\ \\ \sf10(x + 4) = 11(y + 4) \\ \\ \sf10x + 40 = 11y + 44 \\ \\ \bf \large10x - 11y = 4 \: \: \: \:. \:. \: .\: (ii)$

Solving equation (i) and (ii)

$\Large\mathfrak{ \text{W}e\: \: \text{G}et,}$

$\purple{\Large \underline {\boxed{{\bf x = 18\: years} }}} \\ \\ \purple{ \Large  \underline {\boxed{{\bf y = 16\: years} }}}$

Hence,

• Present age of Karan = 18 Years
• Present age of Arjun = 16 Years

$\Large \red{\mathfrak{  \text{W}hich \:   \: are \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswers.}}$

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