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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

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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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