Question

mr.sharma gave 1/5 of his money to his wife half of the remainder to his son and 3/4 of rest to his daughter. if he is left with rs. 4000. what was the total amount he had?

Answer 1

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Answer 2

$Let \: the \: Total \:amout\: of \: mr.sharma = x$

$i) Share \: money \: wife \:get = \frac{x}{5} \: --(1)$

$ii) Remaining \:money = x - \frac{x}{5} \\= \frac{5x-x}{5} \\= \frac{4x}{5} \:--(2)$

$iii) Share \: money \: Son \:get = \frac{1}{2} \times \frac{4x}{5} \\= \frac{2x}{5}\: --(3)$

$iv) Rest \: of \: money \\= \frac{4x}{5} - \frac{2x}{5} \\= \frac{4x-2x}{5} \\= \frac{2x}{5} \:--(4)$

$v) Share \:of \: Daughter \\= \frac{3}{4} \: of \: \frac{2x}{5} \\= \frac{3x}{10} \: ---(5)$

/* According to the problem given */

$x - \frac{x}{5} - \frac{2x}{5} - \frac{3x}{10} = 4000$

$\implies \frac{10x - 2x - 4x - 3x }{10} = 4000$

$\implies \frac{10x - 9x}{10} = 4000$

$\implies \frac{x }{10} = 4000$

$\implies x = 40000$

Therefore.,

$\red{Total \:amout\: of \: mr.sharma}\\\green {=Rs \:40000 }$

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