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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

A woman starts shopping with Rs. X and Y paise, spends Rs. 3.50 and is left with Rs. 2Y and 2 X 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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