Question

Mayank visit 3 shops one by one.At each shop,he spent one third of the money he had at that shop.if he is left with 32 with him after visiting the shops,find the amount of money he had in the beginning.

Answer 1

Let total money he has= x

Money spent on 1st shop= 1/3 of x

=
$\frac{1}{3}x$

Amount left=
$x - \frac{x}{3}$


$= \frac{2x}{3}$


Now on 2nd shop he spent =1/3 of 2x/3


$\frac{2x}{3} \times \frac{1}{3}$

$= \frac{2x}{9}$

Amout left
$= \frac{2x}{3} - \frac{2x}{9 } \\ \\ = \frac{6x - 2x}{9} \\ \\ = \frac{4x}{9}$

Now amount spent on 3rd shop = 1/3 of 4x/9

$= \frac{4x}{9} \times \frac{1}{3} \\ \\ = \frac{4x}{27}$


Amount left
$= \frac{4x}{9} - \frac{4x}{27}$


$= \frac{12x - 4x}{27}$
$= \frac{8x}{27}$


After visiting all the shops he had 8x/27 rupees

But according to the question it is 32

Hence

$\frac{8x}{27} = 32$

$8x = 32 \times 27 \\ \\ 8x = 864 \\ \\ x = \frac{864}{8} \\ x = 108$


Total amount he had i starting =₹108


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