2. Sample Papers
  3. SSC

SSC Sample Paper SSC CGL - Sample Paper-27

  • question_answer
    An egg vendor calls on his first customer and sells half eggs and half an egg. To the second customer, he sells half what he was left with and half an egg and to the third customer, he sells half of what he was then left with and half an egg. However, he did not break any egg. If, in the end, the vendor was left with three eggs, how many eggs did he have initially?

    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.
You will be redirected in 3 sec spinner