Question

An egg vendor calls on his first customer and he sells half his eggs and half an egg. To the second customer, he sells half of what he has 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 did he have initially ?

• A. 26
• B. 31
• C. 39
• D. None of these

Answer 1

The correct option is B 31

Let initial quantity was $x$ .
Firstly, He sells half his eggs and half an egg to first vendor, means
$x/2-0.5$
To the second customer, he sells half of what he has left with and half an egg, and to the third customer, means
$\left(\right(x/2-0.5\left)/2\right)-0.5$
To the third customer, he sells half of what he was then left with and half an egg;
$\left(\right((x/2-0.5)/2)-0.5)/2-0.5$ ,
In the end, the vendor was left with three eggs, Means;
$\left(\right((x/2-0.5)/2)-0.5)/2-0.5=3$ or $x=\left(\right(\left(\right(3.5\times 2)+0.5)\times 2+0.5)\times 2)=31$
Thus Option B is correct answer.