Question

The cost price of two dozen bananas is Rs. 32. After selling 18 bananas at the rate of Rs. 12 per dozen, the shopkeeper reduced the rate as Rs. 4 per dozen. The percent loss is.
a. 25.2%
b. 32.4%
c. 36.5%
d. 37.5%

Answer 1

Hint:In order to solve this question, we should know that one dozen bananas or anything contains 12 pieces of that item. Also, we need to know that percent loss can be calculated by using the formula, loss percentage = $\dfrac{\text{loss}}{\text{cost price}}\times 100$. By using these concepts, we can solve this question.

Complete step-by-step answer:
In this question, we have been given the cost price of 2 dozen bananas as Rs. 32 and it is also given that after selling 18 bananas at the rate of Rs. 12 per dozen, the shopkeeper reduced the rate as Rs. 4 per dozen. And we have been asked to find the percent loss is.
To solve this question, we should know the formula of loss percentage, that is, loss percentage = $\dfrac{\text{loss}}{\text{cost price}}\times 100$. And the loss is calculated by the formula, loss = cost price – selling price.
So, we will first calculate the total loss of the shopkeeper. We have been given that the cost price of 2 dozen bananas is Rs. 32. So, we can say that the cost price of 1 dozen bananas is Rs. $\dfrac{32}{2}$ = Rs. 16, that means, cost price of 12 bananas = Rs. 16, as we know that 1 dozen = 12 bananas.
Now, we have been given that the shopkeeper sold 18 bananas for a selling price of Rs. 12 per dozen, that means, the selling price of 12 bananas is Rs. 12. So, we can say that 1 banana will have the selling price as Rs. $\dfrac{12}{12}$ = Rs. 1. Therefore, we can say that the selling price of 18 bananas is Rs. 1 $\times $ 18 = Rs. 18.
Now, we have been also told that after selling 18 bananas, he reduced the price of bananas to Rs. 4 per dozen. Now, we know that 1 dozen has 12 bananas. So, 2 dozen will have $2\times 12$ = 24 bananas.
Now, after selling 18 out of these 24 bananas, he is left with 24 – 18 = 6 bananas. And it is given that the selling price is reduced to Rs. 4 per dozen. So, the selling price will become Rs. 4 per dozen, that means, selling price will be Rs. 4 for 12 bananas. So, we can say that the selling price for 1 banana will become Rs. $\dfrac{4}{12}$. And therefore, we can say that the selling price of 6 bananas will become Rs. $\dfrac{4}{12}\times 6$ = Rs. 2. Hence, we can say that he sold the last 6 bananas for Rs. 2.
Therefore, we can say that the selling price of 2 dozen = 24 bananas is the sum of the selling price of the first 18 bananas and the selling price of the next 6 bananas, that is Rs. 18 + Rs. 2 = Rs. 20.
Therefore, the total selling price of 2 dozen bananas is Rs. 20.
Now, we know that loss is calculated as, cost price – selling price.
So, we can say that, loss on 2 dozen bananas = Rs. 32 – Rs. 20 = Rs. 12.
Now, we will put the value of loss and cost price in the loss percentage formula, that is,
Loss percentage = $\dfrac{\text{loss}}{\text{cost price}}\times 100$
Loss percentage = $\dfrac{12}{32}\times 100$
And, we can further write it as,
Loss percentage = 37.25%
Therefore, the shopkeeper had a percentage loss of 37.25%
 Hence, option (d) is the correct answer.

Note: While solving this question, the possible mistake one can make is calculation mistake as the solution has a lot of calculation. Also, we can make mistakes at the point where the selling price is reduced to Rs. 4 per dozen, which means the new selling price is Rs. 4 per dozen. One might make a mistake by writing the new selling price as Rs (12 - 4) = Rs. 8, which is wrong and will give the wrong answer.