33 C
Maharashtra
Friday, June 9, 2023
HomeCSIRUGC NETA woman starts shopping with Rs. X and Y paise, spends Rs....

# 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

## 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

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.
RELATED ARTICLES

### Any two closed subset of metric space are connected iff they are disjoint

$${}$$