Question

A man bought a number of clips at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20%?
(a) 4
(b) 5
(c) 6
(d) 7

Answer 1

Hint: In this question, the cost price can be calculated by assuming the total number of clips of each type bought to be 6 so that the total number of clips becomes 12. We can then sum over the respective costs of the clips to obtain the total cost price. Thereafter, we can take the selling price per dozen to be x and using the formula for profit percentage, we can determine the value of x which will be the answer to this question.

Complete step-by-step answer:

In this question, we are given the profit percentage and not the value of the profit. Therefore, the exact number of clips bought is not required to be calculated. Therefore, as we have to find the price per dozen of the clips, we can take the number of clips bought of each type to be 6 so that the total number of clips bought is 12.

Therefore, for a total of 12 clips (6 of each type). Now,

Cost of 3clips of the first type = Rs.1
Cost of 1clip of the first type = Rs.${\displaystyle \frac{1}{3}}$.....(1.1)

And

Cost of 2clips of the second type = Rs.1
Cost of 1clip of the second type = Rs.${\displaystyle \frac{1}{2}}$.....(1.2)

Thus as 6 clips are brought from each type,

$$\text{Total Cost}\text{ Price= }Rs.{\displaystyle \frac{1}{3}}\times 6+Rs.{\displaystyle \frac{1}{2}}\times 6=Rs.5........(1.3)$$

Let the selling price per dozen be $Rs.x$. Therefore, as 12 clips are sold,

$\text{Total Selling Price}=Rs.x.........(1.4)$

Now, the formula for profit percentage is

$\text{Profit Percentage=}{\displaystyle \frac{\text{Total Selling Price-Total Cost Price}}{\text{Total Cost Price}}}\times 100...........(1.5)$

The profit percentage is given to be 20. Therefore, from equations (1.3), (1.4) and (1.5), we obtain

 $\begin{array}{rl}& \text{20=}{\displaystyle \frac{Rs.x-Rs.5}{Rs.5}}\times 100\\ & \Rightarrow x={\displaystyle \frac{5\times 20}{100}}+5=6\end{array}$

Thus, we obtain the answer to be 6 which matches option (c) and hence (c) is the correct answer.

Note: In this case, we assumed that a total of 12 clips were brought, however we can assume the total number of clips to be any number such as 100. However, as the profit percentage does not change with the total number of items bought, the answer would be the same in all the cases regardless of the total number of clips bought.