| At a dinner party, every two guests used a bowl of rice between them, every three guests used a bowl of dal among them and every four guest used a bowl of curd among them. There are altogether 65 bowls. What is the number of guests present at the party? |
A) 90
B) 80
C) 70
D) 60
Correct Answer: D
Solution :
| Let the number of guests while 2 at a time\[=x\] |
| Let the number of guests while 3 at a time \[=y\] |
| Let the number of guests white 4 at a time \[=z\] |
| \[\therefore \] \[x+y+z=65\] ... (i) |
| We have, \[2x=3y=4z\] |
| Number of guests, ... (ii)\[y=\frac{2x}{3}\]\[\Rightarrow \]\[z=\frac{2}{4}x=\frac{1}{2}x\] |
| \[\therefore \]From Eq. (i), |
| \[x+\frac{2x}{3}+\frac{1}{2}x=65\] |
| \[\Rightarrow \]\[\frac{6x+4x+3x}{6}=65\]\[\Rightarrow \]\[x=30\] |
| \[\therefore \]Number of guests \[=2x=2\times 30=60\] |
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