Question

Given, 11 oranges are bought for Rs. 10 and 10 oranges are sold for Rs. 11. Find the gain/loss percent.
(a) 21% loss
(b) 11% gain
(c) 21% gain
(d) 11% loss

Answer 1

Hint: Find the cost price and selling price of 1 orange from the given information. If selling price is greater than cost price then apply the formula, $gain\mathrm{\%}={\displaystyle \frac{\text{gain on one orange}}{\text{cost price of one orange}}}\times 100\mathrm{\%}$ and if cost price is more then apply the formula, $loss\mathrm{\%}={\displaystyle \frac{\text{loss on one orange}}{\text{cost price of one orange}}}\times 100\mathrm{\%}$.

Complete step by step answer:
Let us understand the cost price (C.P) and selling price (S.P) first.
Cost price is the price at which an article is purchased whereas selling price is the price at which an article is sold. If the cost price of an article is more than its selling price then we say that loss occurs and if selling price of an article is more than its cost price then we say that gain or profit occurs.
Now, let us come to the question.
Cost price for 11 oranges $=Rs.\text{ 10}$
Therefore, cost price of 1 orange $=Rs.{\displaystyle \frac{10}{11}}$
Now, selling price of 10 oranges $=Rs.\text{ 11}$
Therefore, selling price of 1 orange $=Rs.{\displaystyle \frac{11}{10}}$
We can clearly see that the selling price of one orange is more than the cost price of one orange, therefore, we can say that gain occurs.
Now, gain on one orange $=\text{S}\text{.P of one orange}-\text{C}\text{.P of one orange}=Rs.({\displaystyle \frac{11}{10}}-{\displaystyle \frac{10}{11}})$.
Therefore,
$\begin{array}{rl}& gain\mathrm{\%}={\displaystyle \frac{\text{gain on one orange}}{\text{cost price of one orange}}}\times 100\mathrm{\%}\\ & ={\displaystyle \frac{({\displaystyle \frac{11}{10}}-{\displaystyle \frac{10}{11}})}{{\displaystyle \frac{10}{11}}}}\times 100\mathrm{\%}\\ & =({\displaystyle \frac{{\displaystyle \frac{11}{10}}}{{\displaystyle \frac{10}{11}}}}-1)\times 100\mathrm{\%}\\ & =({\displaystyle \frac{121}{100}}-1)\times 100\mathrm{\%}\end{array}$
Taking, L.C.M, we get,
$\begin{array}{rl}& gain\mathrm{\%}=\left({\displaystyle \frac{121-100}{100}}\right)\times 100\mathrm{\%}\\ & =21\mathrm{\%}\end{array}$

Hence, option (c) is the correct answer.

Note:
Here, as you can see, 11 oranges were purchased and 10 items were sold. So, the number of items purchased is not equal to the number of items sold. Therefore, we cannot take the difference directly to gain an amount. We must deal with the same number of oranges bought and sold, so, we found the C.P and S.P of one orange and then the gain %. Also, to find gain% or loss%, always take the cost price in the denominator.