Question

Bob the baker has two options. He can either run a small bakery by himself or run a larger bakery in an equal partnership with three more bakers. If the daily profit from the larger bakery is thrice that of the smaller bakery, which bakery should Bob run so that he gets more profit for himself?

• A. Smaller bakery
• B. Larger bakery
• C. Both bakeries earn the same profit for Bob.
• D. Cannot be determined.

Answer 1

The correct option is A Smaller bakery

Let the profit from the smaller bakery be "P".

$Option1:\text{Small Bakery}$

$\text{Daily profit = P}$

$\text{Bob is the sole owner of the smaller}\text{bakery}$

$⟹\text{Number of owners}=1$

$\text{Profit earned by each owner}=\frac{P}{1}=P$

$Option2:\text{Large Bakery}$

$\text{Daily profit of the larger bakery is thrice}\text{that of the smaller bakery}$

$⟹\text{Daily profit}=3\times P$

$\text{Bob runs the larger bakery in equal}\text{partnership with three other bakers.}$

$⟹\text{Number of owners}=1+3=4$

$\text{Profit earned by each owner}=\frac{3\times P}{4}=\frac{3}{4}\times P$

$\text{When a number or fraction is multiplied}\text{by a fraction less than 1, then the resulting}\text{product will also be less than 1.}$

$⟹(\frac{3}{4}\times P)<P$

$\therefore \text{Bob would earn more profit running a}$ $\text{smaller bakery by himself.}$