Question

11. A man gave 2/5 of his money to his son, 40% of the remainder to his daughter and the remaining money to his wife. If the son got 3000 more than his daughter, how much did his wife receive?


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Answer 1

$\\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Let man has 'x' money.

He gave 2/5 of his money to son.

Son has 2x/5 money.

Remaining money = x - 2x/5

Remaining money = 3x/5

He gave 40% of the remaining money to her daughter.

$\\ \implies \sf \: \frac{40}{100} \times \frac{3x}{5} \\ \\ \implies \sf \: \frac{120x}{500}$

daughter has 120x/500 money.

Rest is with his wife.

$\\ \implies \: \sf \: x - \frac{2x}{5} - \frac{120x}{500} \\ \\ \implies \sf \: \frac{500x - 200x - 120x}{500} \\ \\ \implies \sf \: \frac{ 180x }{500} \\ \\ \implies \sf \: \frac{9x}{25}$

his wife has 9x/25 money.

Also,

Son has 3000 more than daughter.

$\ \\ \\ \sf \: \frac{2x}{5} = 3000 + \frac{120x}{500} \\ \\ \\ \sf \: \frac{2x}{5} - \frac{120x}{500} = 3000 \\ \\ \\ \sf \: \frac{200x - 120x}{500} = 3000 \\ \\ \\ \sf \: \frac{80x}{500} = 3000 \\ \\ \\ \sf \: x = \frac{3000 \times 500}{80} \\ \\ \\ \boxed{ \sf \: x = 18750}$

Therefore , man has 18750 money.

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His wife has 9x/25 money.

Putting x = 18750, we get..

$\\ \\ \implies \sf \: \frac{9(18750)}{25} \\ \\ \\ \implies \sf \: 6750$

$\\ \therefore \boxed{\: \sf \: \orange{wife \: has \: 6750 \: money.}}$