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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

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

If â€‹\( Y>50 \)â€‹Â then according to the information given,

â€‹\( Y-50=2X \)â€‹ and â€‹\( X-3=2Y \)â€‹

â€‹\( \therefore 2X-Y=-50 \)â€‹Â ………… (1)

Â and â€‹\( X-2Y=3 \)â€‹Â ……………… (2)

equation (1) – 2â€‹\( \times \)â€‹ equation (2) gives,

â€‹\( 3Y=-56 \)â€‹Â which is absurd as Y is positive.

Now, if â€‹\( Y<50 \)â€‹Â thenÂ according to the information given,

â€‹\( 100+Y-50=2X \ and \ X-1-3=2Y \)â€‹

â€‹\( \therefore 2X-Y=50 \)â€‹Â …………. (3)

and â€‹\( X-2Y=4 \)â€‹Â ………………… (4)

equation (3) – 2â€‹\( \times \)â€‹ equation (4) gives,

â€‹\( 3Y=42 \)â€‹

\( \implies Y=14 \)

\therefore from (4),

â€‹\( X=32 \)â€‹

â€‹\( \therefore \)â€‹Â The amount she started with is Rs. 32.14.

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