Question

Mayank visits three shops one by one. At each shop, he spends two thirds of the money he had at that shop.If he is left with rs. 32 with him in the end after visiting all 3 of them. Find the amount of money he had in the beginning.

Answer 1

Let X be the money he had earlier

Then At the 1st shop he spent
$\frac{2x}{3}$
money left =
$x - \frac{2x}{3} = \frac{x}{3}$
At 2nd shop he spent 2/3rd of money he had i.e
$\frac{x}{3} \times \frac{2}{3} = \frac{2x}{9}$
Money left =
$\frac{x}{3} - \frac{2x}{9} = \frac{x}{9}$
money spent in 3rd shop =
$\frac{x}{9} \times \frac{2}{3} = \frac{2x}{27}$
money left =
$\frac{x}{9} - \frac{2x}{27} = \frac{x}{27}$
Then According to question he had 32 rs now

means,

$(x) - ( \frac{2x}{3} + \frac{2x}{9} + \frac{2x}{27} ) = 32$
$x = 864$
So he had 864$