Question

A vendor purchased bananas at Rs. 40 per dozen and sold them at 10 for Rs 36. Find his gain.

Answer 1

Hint: Hint: Here, we will find the gain percentage. First, we will find the cost Price and selling Price for an equal number of bananas. Then using the formula, we will find the profit gained by the vendor. Then we will find the profit percentage by using the formula. The profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.

Formula used: We will use the following formulas:
Profit or Gain $$=$$ Selling Price $$-$$ Cost Price
Profit Percentage$$={\displaystyle \frac{P}{CP}}\times 100\mathrm{\%}$$, where $$P$$ is the profit and $$CP$$ is the cost price.

Complete step-by-step answer:
We will first find the cost price of 1 banana. We are given the cost price of 12 bananas.
Cost price of $$12$$ Bananas $$=\mathrm{R}\mathrm{s}.40$$
We can find the cost price of 1 banana by dividing the total cost by the number of bananas.
Cost price of $$1$$ Banana$$=\mathrm{R}\mathrm{s}.{\displaystyle \frac{40}{12}}$$
$$\Rightarrow$$ Cost price of $$1$$ Banana$$=3.33$$
We will find the selling price of 1 banana
We are given the selling price of 12 bananas.
Selling price of $$10$$ Bananas$$=\mathrm{R}\mathrm{s}.36$$
To find the selling price of 1 banana can be found by dividing the total cost by the number of bananas.
Selling price of $$1$$ Banana$$=\mathrm{R}\mathrm{s}.{\displaystyle \frac{36}{10}}$$
$$\Rightarrow$$ Selling price of $$1$$ Banana$$=\mathrm{R}\mathrm{s}3.6$$
Now we will find the selling price of 12 bananas by multiplying 12 to selling price of 1 banana. Therefore we get
Selling price of $$12$$ Bananas$$=\mathrm{R}\mathrm{s}.3.6\times 12=\mathrm{R}\mathrm{s}.43.2$$
Profit can be found only when the cost price and selling price are for equal amounts. Thus, we will find the profit amount by subtracting the cost price from the selling price.
Profit$$=$$ Selling Price$$-$$ Cost Price
Substituting the values of selling and cost price, we get
$$\Rightarrow$$ Profit$$=\mathrm{R}\mathrm{s}.\left(43.2-40\right)$$
$$\Rightarrow$$ Profit$$=\mathrm{R}\mathrm{s}.3.2$$
Now we will calculate the profit percentage. We know tha,
Substituting the value of profit and cost price in the formula $$\mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}={\displaystyle \frac{P}{CP}}\times 100\mathrm{\%}$$
$$\Rightarrow \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}={\displaystyle \frac{3.2}{40}}\times 100$$
$$\Rightarrow \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}={\displaystyle \frac{32}{4}}$$
Dividing 32 by 4, we get
$$\Rightarrow \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}=8\mathrm{\%}$$
Therefore, the gain is Rs.$$3.2$$ and the profit percentage is $$8\mathrm{\%}$$.

Note: We can explain profit better in terms of cost price and selling price. Cost price is the actual price of the product or commodity and selling price is the amount at which the product is sold. So, if the selling price of the commodity is more than the cost price, then the business has gained its profit. We should remember that for profit, the selling price is more than the cost price. Cost price and selling price is calculated for equal commodities. The percentage value for profit is calculated in terms of cost price.