Question

A boy spends 3/4 of his pocket money and then 4/5 of the remainder is given to his sister. If he has $40 left, what did he have at first ?​

Answer 1

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Let the money he had first be x

He spends $\frac{3}{4} \: of \: x$ of his pocket money(x)

$x-\frac{3}{4}x$= remaining money he had

$\frac{4x-3x}{4}=\frac{x}{4}$

From this money he gave $\frac{4}{5} \: of \: \frac{-x}{4}=\frac{x}{5}$

The remaining money he had is 40$ = he spent - he gave to his sister

$\frac{x}{4} - \frac{x}{5} = 40$

$\frac{5x - 4x}{20} = 40$

$\frac{x}{20} = 40$

$x = 40 \times 20 = 800$

∴ His pocket money is 800$