Question

A tea-stall owner bought 2 dozen fruitcakes at rupees 4 each and sold them all earning a profit of 50%. How much profit did the tea-stall owner make?

Answer 1

Hint:First we need to convert dozen numbers into actual numbers. Then, find the cost price with the help of the price of one cake. Further calculate the profit at cost price with help of profit percent i.e 50%.

Complete step-by-step answer:
In this question we have,
Cost price of one fruit cake = Rs 4
Total number of fruit cake = 2 dozen
Profit percentage = 50%
Now, we find the total number of fruit cakes in two dozen.
As we know that 1 dozen = 12 fruit cakes
So, multiple 2 by 12 to get total number of cakes,
2 dozen = $2 \times 12 = 24$ fruit cakes
 $ \Rightarrow $ 2 dozen = 24 fruit cakes

Now, we have to find the cost price of these 24 fruit cakes,
Cost of 1 cake = Rs 4
So, cost of 24 cakes will be,
= $4 \times 24 = 96$ (multiply 24 by 4 to get total cost)
Cost price of 2 dozen cakes = Rs 96.
We know the formula, $\text{Profit percentage}$ = ${\dfrac{\text{Profit}}{\text{Cost Price}}}\times 100$
Profit percentage = 50% , Cost price = 96
Substituting in above formula we get
$\text{Profit percentage}$ = ${\dfrac{\text{Profit}}{\text{Cost Price}}}\times 100$
$50$ = ${\dfrac{\text{Profit}}{96}}\times 100$
$\text{Profit} = {\dfrac{50}{100}}\times 96$
$\text{Profit} = {\dfrac{1}{2}}\times 96$
$\text{Profit} = 48$

$\therefore $ Tea-stall owner will make the profit amount of Rs 48.

Note:This question is based on a simple arithmetic question of Profit – Loss type. In such questions percentage calculations are always playing an important role.Students should remember the formulas i.e $\text{Profit = sell price – cost price}$ and $\text{Loss = cost price – sell price}$,$\text{Profit percentage}$ = ${\dfrac{\text{Profit}}{\text{Cost Price}}}\times 100$ and $\text{Loss percentage}$ = ${\dfrac{\text{Loss}}{\text{Cost Price}}}\times 100$ for solving these types of questions.