Question

Oranges are bought at 100 for Rs. 80 and all of them are sold at 80 for Rs. 100. Find the loss or gain as percent in this transaction.

Answer 1

Hint: Determine the cost price of one orange and the selling price of one orange and use the formula \[\dfrac{{SP - CP}}{{CP}} \times 100\% \] to find the loss or gain percent of the orange.

Complete step-by-step answer:
Cost price of an object is the price at which it is bought.
The selling price of an object is the price at which it is sold.
The gain or loss is the difference in the selling price and the cost price of the object.

In this problem it is given that the oranges are bought at 100 for Rs. 80 which means that 100 oranges are bought at Rs. 80.
Then the cost price of each orange is Rs. 80 divided by 100.
\[CP = \dfrac{{80}}{{100}}\]
\[CP = Rs.0.8...........(1)\]
It is also given that all the oranges are sold at 80 for Rs. 100 which means that 80 oranges are sold at Rs. 100.
Then the selling price of each orange is Rs. 100 divided by 80.
\[SP = \dfrac{{100}}{{80}}\]
\[SP = Rs.1.25..........(2)\]
We observe that the selling price of each orange is more than its cost price, hence, it is a gain.
The gain of each orange is the difference between its selling price and cost price.
Gain = SP – CP
Gain = 1.25 – 0.8
Gain = Rs. 0.45
The gain percent is the percentage of gain to its cost price, hence, it is given as follows:
\[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% \]
Substituting the values into the above equation, we have:
\[Gain\% = \dfrac{{0.45}}{{0.8}} \times 100\% \]
\[Gain\% = 56.25\% \]
Hence, the percentage gain is 56.25 %.

Note: You can also calculate the cost price and selling price for 100 oranges and then calculate the gain percent, it will give you the same answer.For 100 oranges Selling price will be Rs125 and cost price for 100 oranges is Rs.80.Here, Selling price of an orange is more than cost price So it is gain and then calculate gain % using formula \[Gain\% = \dfrac{{Gain}}{{CP}} \times 100\% \].