Question

A vendor purchased 40 dozen 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 to make a profit of 20%.

Answer 1

Hint: Here we go through by finding the gain by taking the gain% on the cost price of all the bananas and then add this gain to the cost price of the banana to find out the selling price of all the bananas.

Complete Step-by-Step solution:
Here in the question it is given that,
Cost price of 40 dozen bananas=Rs.250
We know that there are 12 banana in one dozen,
Therefore the total amount of bananas $ = 12 \times 40 = 480$.
In which 30 banana gets rotten therefore the number of good banana=480-30=450 banana
Now we have to calculate a total gain of 20% by selling the good banana.
So we have to find 20% of the cost price of bananas I.e. Gain=20% of C.P $\dfrac{{20}}{{100}} \times 250 = Rs.50$
Now we know that S.P =C.P + Gain =Rs.250+Rs.50=Rs.300, (Here S.P means selling price and C.P means cost price).
So S.P of 450 bananas= Rs.300.
No we have to find the price of per doze banana means price of 12 banana, for finding this we apply unitary method so first we find out the price of one banana by dividing the total price by the total no of banana i.e. selling price of one banana$ = \dfrac{{300}}{{450}}$
And for finding the price of 12 banana we multiply 12 by the price of one banana
i.e. S.P of 12 bananas$ = \dfrac{{300}}{{450}} \times 12 = Rs.8$
Hence the vendor should sell the remaining bananas at the rate Rs.8 per dozen to make a profit of 20%.

Note: Whenever we face such types of problems always start thinking about the cost price, selling price , gain and loss questions are mainly focused on these points so write separately all these data what are given in the question and what you have to find and then apply the formula to find out the unknown terms. By doing that way you easily get the answer and also less chances for making mistakes.