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.

Nice

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