A man spends `1/2` of his money in one shop, `2/3` of the remainder in another shop and `4/5` of what is left he goes away. If he has Rs. 10 still left, how much did he have at first.

Explanation

Let the total money man have Rs. x

Man spends = x/2

Remaining money = `x - x/2 = x/2`

Man spends in shop= `2/3 xx x/2 = x/3`

Left money = `x/2 - x/3 = x/6`

Money goes away = ` 4/5 xx x/6 = (2x)/(15) `

Now, Left money = `x/6 - (2x)/(15) = (5x - 4x)/(30) = x/(30)`

`:. x/30 = 10`

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