Question

Raj gave 5/14 of his money to his son, 2/3 of the remaining to his daughter and the rest to his wife. If the wife got `36,000, what was the total amount?

Answer 1

Let the total money be x.

Therefore ,

Raj gave $\bold{\frac{5}{14}}$ of money to his son = $\bold{\frac{5x}{14}}$

Raj gave 2/3 of remaining to his daughter.

So,

Remaining money,

= $\bold{x-\frac{5x}{14}}$

= $\bold{\frac{14x-5x}{14}}$

= $\bold{\frac{9x}{14}}$

$\therefore\bold{Remaining\:money\:=\frac{9x}{14}}$

He gave 2/3 of remaining = 2/3 of 9x/14

= $\bold{\frac{2}{3}\times\frac{9x}{14}}$

= $\bold{\frac{18x}{42}}$

= $\bold{\frac{3x}{7}}$

$\therefore\bold{Remaining\:money\:=\frac{3x}{7}}$

Therefore,

$\implies\bold{x-(\frac{5}{14}+\frac{3}{7})=36000}$

$\implies\bold{x-(\frac{5x+6x}{14})=36000}$

$\implies\bold{x-(\frac{11x}{14})=36000}$

$\implies\bold{\frac{14x-11x}{14}=36000}$

$\implies\bold{\frac{3x}{14}=36000}$

$\implies\bold{3x=504000}$

$\boxed{\bold{\therefore\:x=168000}}$

$\boxed{\bold{\therefore{Total\:amount\:of\:money\:=Rs\:168000}}}$