Question

Manthan's age is 9/11th of his brother's age and the age of Manthan's father is

23 years more than the age of Manthan. If the average age of Manthan, Manthan's

father and Manthan's brother is 27 years, find the age of Manthan.
?​

Answer 1

☯ GIVEN :

• The age of Manthan is 9/11 of his brother's age.

• The age of Manthan's father is 23 years more than the age of Manthan.

• The average age of Manthan, Manthan's father and Manthan's brother is 27 years.

☯ TO FIND :

• Manthan's age.

➲SOLUTION :

Let the age of Manthan's brother be x years.

• The age of Manthan is 9/11 of his brother's age.

Then, the age of Manthan = x×9/11 = 9x/11 years.

• The age of Manthan's father is 23 years more than the age of Manthan.

The age of Manthan's father = (9x/11)+23 years.

• The average age of Manthan, Manthan's father and Manthan's brother is 27 years.

We know that,

$\bigstar{ \underline{\boxed{ \ \red{ \tt{Average \: Age = \dfrac{Total \: sum \: of \: ages}{Total \: persons} }}}}} \bigstar$

Substituting the values :

$\implies {\sf{Average \: Age = \dfrac{Total \: sum \: of \: ages}{Total \: persons}}}$

$\implies{\sf{27= \dfrac{x + \dfrac{9x}{11} + \bigg( \dfrac{9x}{11} + 23 \bigg) }{3}}}$

$\implies{\sf{27= \dfrac{x + \dfrac{9x}{11} + \bigg( \dfrac{9x +253 }{11 } \bigg) }{3}}}$

$\implies{\sf{27= \dfrac{x + \dfrac{9x}{11} + \dfrac{9x +253 }{11 } }{3}}}$

$\implies{\sf{27= \dfrac{ \dfrac{11x + 9x + 9x + 253}{11} }{3}}}$

$\implies{\sf{27= \dfrac{ \dfrac{29x+ 253}{11} }{3}}}$

$\implies{\sf{27 \times 3= \dfrac{29x + 253}{11} } }$

$\implies{\sf{81= \dfrac{29x + 253}{11} } }$

$\implies{\sf{81 \times 11= 29x + 253} }$

$\implies{\sf{891 - 253 =29x }}$

$\implies{\sf{638=29x }}$

$\implies \sf{ x = \cancel{ \dfrac{638 }{ 29}}}$

$\implies \underline{\huge {\boxed{\red{\bf{ x =22 }}}}}$

$\huge{\pink{\therefore}}$ Manthan's age = 22×9/11 = 18 years.

Answer 2

Manthan's age is (9/11)th of his brother's age. So the brother's age is (11/9)th of Manthan's age.

And Manthan's father is 23 years older than Manthan.

Let Manthan's age be x. Then,

• Manthan's brother's age = (11/9)x

• Mathan's father's age = x + 23

Given that the average age of Manthan, Manthan's brother and Manthan's father is 27, i.e.,

$\sf{\longrightarrow\dfrac{x+\dfrac{11x}{9}+x+23}{3}=27}$

$\sf{\longrightarrow2x+\dfrac{11x}{9}+23=27\times3}$

$\sf{\longrightarrow\dfrac{29x}{9}+23=81}$

$\sf{\longrightarrow\dfrac{29x}{9}=58}$

$\sf{\longrightarrow x=58\times\dfrac{9}{29}}$

$\sf{\longrightarrow\underline{\underline{x=18}}}$

I.e., Manthan is 18 years old.