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# A vendor purchased 40 dozens bananas for Rs. 250. Out of these 30 bananas were rotten and could not be sold. At what rate per dozen, should he sell the remaining bananas to make a profit of 20%?A) Rs. 4B) Rs. 6C) Rs. 8D) Rs. 10

Hint: First of all, find the selling price of all the bananas at a profit of 20%. Next, subtract the number of rotten bananas from all the bananas to find the number of bananas that can be sold. Hence, find the price of bananas by dividing the total cost by the number of bananas that can be sold.

Complete step by step solution: We are given that cost price (C.P.) of 40 dozens of bananas is Rs. 250.
As we know that there are 12 bananas in 1 dozen.
Then, calculate the total number of bananas by multiplying 12 with 40.
Hence, $12 \times 40 = 480$ bananas cost Rs. 250.
We want to find the selling price (S.P.) of the when profit is 20%
Then, $\text{SP} = \dfrac{\text{CP} \times \left( 100+ \text{profit %} \right)}{100}$
${\text{SP}} = \dfrac{{{\text{250} \times }\left( {{\text{100 + 20}}} \right)}}{{{\text{100}}}} \\ \Rightarrow {\text{SP}} = \dfrac{{250 \times \left( {120} \right)}}{{100}} \\ \Rightarrow {\text{SP}} = 300 \\$
But, 30 bananas were rotten, hence the number of good bananas are $480 - 30 = 450$
That is, 450 bananas are sold at the rate of Rs. 300
Now, we will calculate the price of 1 banana by dividing the total cost by the number of bananas to be sold.
$\Rightarrow \dfrac{{300}}{{450}}$
Next, multiply the price of 1 banana with 12 to find the price of 1 dozen bananas.
Thus,
$\Rightarrow \dfrac{{300}}{{450}} \times 12 = 8$

Therefore, bananas should be sold at the rate of Rs. 8 per dozen in order to gain a profit of 20%.

Note: The price at which the goods are bought is known as cost price and the price at which the goods are sold, the price is known as selling price. In this question, the price of rotten bananas will be included in cost price, but it is important to exclude that number from the selling price.