Question

A man buys some toffees at 5 toffees for 3 rupees and the same number of toffees at 5 toffees for Rs 4. He sold them at 5 toffees for 4 rupees. Find his overall gain or loss percentage?

Answer 1

Hint:
Here, we will find the sale price and cost price. Then we will check if the costing price is greater than the selling price of the shopkeeper in Bhopal, then find the gain or loss percentage using \[{\text{Loss/Gain}}\% = \dfrac{{{\text{Loss/Gain}}}}{{{\text{C.P.}}}} \times 100\] from the given values.

Complete step by step solution:
We are given that man buys some toffees at 5 toffees for 3 rupees and the same number of toffees at 5 toffees for Rs 4. Then he sold them at 5 toffees for 4 rupees.
We will now find the amount at which the man sells the toffees is by multiplying 14 by 4, we get
\[
  {\text{S.P.}} = 10 \times 4 \\
   = {\text{Rs }}40 \\
 \]
We will now find the total C.P. which the man buys from the given conditions, we get
\[
  {\text{C.P.}} = 5 \times 3 + 5 \times 4 \\
   = {\text{Rs }}35 \\
 \]
Thus, the cost price is Rs 35.
Since we know that the selling price is greater than the selling price, there is a profit.
We know that the profit is calculated by the difference in the cost price of an article from selling price of an article.
Subtracting the values of cost price \[{\text{C.P.}}\] of the shopkeeper in Bhopal from the selling price \[{\text{S.P.}}\] in Bhopal to find the profit of a given article, we get
\[
  {\text{Profit}} = 40 - 35 \\
   = {\text{Rs 5}} \\
 \]
We know that the formula to calculate the profit percentage is calculated as \[{\text{Profit}}\% = \dfrac{{{\text{Profit}}}}{{{\text{C.P.}}}} \times 100\], where C.P. is the cost price.
Substituting the values of Profit and C.P. of a shopkeeper in Bhopal in the above formula for profit percentage of the given article, we get
\[
  {\text{Profit}}\% = \dfrac{5}{{35}} \times 100 \\
   = \dfrac{1}{7} \times 100 \\
   = \dfrac{{100}}{7}\% \\
 \]
Simplifying the above fraction to find the profit percentage, we get
\[{\text{Profit}}\% = 28\dfrac{4}{7}\% \]
Thus, we get that the profit from an article is \[28\dfrac{4}{7}\% \].

Hence, the option is B will be correct.

Note:
While solving these types of problems, the amount of discount given on the marked price is \[\dfrac{{{\text{Discount Percentage}}}}{{100}} \times {\text{Marked Price}}\] and then this amount is subtracted from the market price in order to get the selling price. In this question, students must note that we have added all the expenses of transportation and travelling while finding the cost price of an article. So this point must be taken care of.