Question

A thief steals half the total no of loaves of bread plus 1/2 loaf from a bakery. A second thief steals half the remaining no of loaves plus 1/2 loaf and so on. After the 5th thief has stolen there are no more loaves left in the bakery. What was the total no of loaves did the bakery have at the beginning

Answer 1

The bakery had total 31 loaves of bread at the beginning.

Explanation

Suppose, the total number of loaves, the bakery had at the beginning was  $x$

First thief steals half the total number of loaves  plus 1/2 loaf. So, the remaining number of loaves after first thief $=x-(\frac{x}{2}+\frac{1}{2})=\frac{x}{2}-\frac{1}{2}=\frac{x-1}{2}$

Second thief steals half the remaining number of loaves plus 1/2 loaf. So, the remaining number of loaves after second thief $=\frac{x-1}{2}-(\frac{x-1}{4}+\frac{1}{2})=\frac{x-1}{4}-\frac{1}{2}= \frac{x-3}{4}$

Like this way......

Remaining number of loaves after third thief $=\frac{x-3}{4}-(\frac{x-3}{8}+\frac{1}{2})=\frac{x-3}{8}-\frac{1}{2}=\frac{x-7}{8}$

Remaining number of loves after fourth thief $=\frac{x-7}{8}-(\frac{x-7}{16}+\frac{1}{2})=\frac{x-7}{16}-\frac{1}{2}=\frac{x-15}{16}$

Remaining number of loves after fifth thief $=\frac{x-15}{16}-(\frac{x-15}{32}+\frac{1}{2})=\frac{x-15}{32}-\frac{1}{2}=\frac{x-31}{32}$

Given that, after the 5th thief has stolen, there are no more loaves left in the bakery. That means......

$\frac{x-31}{32}=0\\ \\ x-31=0\\ \\ x=31$

Thus, the total number of loaves, the bakery had at the beginning was 31.

Answer 2

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