A) 26
B) 31
C) 39
D) None of these
Correct Answer: B
Solution :
Suppose, the vendor initially has x eggs with him. Then, eggs sold to 1st customer \[=\left( \frac{1}{2}x+\frac{1}{2} \right)\] Remaining eggs \[=x-\left( \frac{1}{2}x+\frac{1}{2} \right)=\left( \frac{1}{2}x-\frac{1}{2} \right).\] Eggs sold to 2nd customer \[=\frac{1}{2}\left( \frac{1}{2}x-\frac{1}{2} \right)+\frac{1}{2}=\left( \frac{1}{4}x+\frac{1}{4} \right),\] Remaining eggs \[=\left( \frac{1}{2}x-\frac{1}{2} \right)-\left( \frac{1}{4}x+\frac{1}{4} \right)=\left( \frac{1}{4}x-\frac{3}{4} \right)\] Eggs sold to 3rd customer \[=\frac{1}{2}\left( \frac{1}{4}x-\frac{3}{4} \right)+\frac{1}{2}=\left( \frac{1}{8}x+\frac{1}{8} \right),\] Remaining eggs \[=\left( \frac{1}{4}x-\frac{3}{4} \right)-\left( \frac{1}{8}x+\frac{1}{8} \right)=\left( \frac{1}{8}x-\frac{7}{8} \right)\] \[\therefore \] \[\frac{1}{8}x-\frac{7}{8}=3\] \[\Rightarrow \] \[\frac{1}{8}x=3+\frac{7}{8}=\frac{31}{8}\] \[\Rightarrow \] \[x=\left( \frac{31}{8}\times 8 \right)=31\]You need to login to perform this action.
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