# A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The amount she started with is

## Question:

A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2X paise. The amount she started with is
1. Rs. 48.24
2. Rs. 28.64
3. Rs. 32.14
4. Rs. 23.42

## Answer:

If $Y>50$ then according to the information given,
$Y-50=2X$ and $X-3=2Y$
$\therefore 2X-Y=-50$ ............ (1)
and $X-2Y=3$ .................. (2)
equation (1) - 2$\times$equation (2) gives,
$3Y=-56$ which is absurd as Y is positive.
Now, if $Y<50$ then according to the information given,
$100+Y-50=2X$ and $X-1-3=2Y$
$\therefore 2X-Y=50$ ............. (3)
and $X-2Y=4$ ..................... (4)
equation (3) - 2$\times$equation (4) gives,
$3Y=42$
$\implies Y=14$
$\therefore$ from (4),
$X=32$
$\therefore$ The amount she started with is Rs. 32.14.

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