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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. 48.24Â Â Â Â Â Â Â Â Â Â
2. Rs. 28.64
3. Rs. 32.14Â Â Â Â
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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