Question

If 11 mangoes are bought for Rs. 10 and sold at 10 for Rs. 11. What was the gain or loss %?
(a) 24 %
(b) 21 %
(c) 26 %
(d) 25 %

Answer 1

Hint: In order to find the gain or loss %, first we have to find the cost price of 10 mangoes and the selling price of 10 mangoes. We will do this by using the concept of the unitary method. After that, we see that we have gain or loss. Once we have that, we will calculate its percentage by using the formula
\[\text{Gain Percent}=\dfrac{\text{Gain}}{CP}\times 100\]

Complete step-by-step answer:
Now, we are given that 11 mangoes are bought for 10 Rs. This means that we have,
Cost of 11 mangoes = Rs. 10
Therefore, by applying the unitary method, we have,
Cost of 1 mango \[=\dfrac{10}{11}\]
Cost of 10 mangoes \[=\dfrac{10}{11}\times 10=\dfrac{100}{11}\]
We get the cost price of 10 mangoes as \[Rs.\dfrac{100}{11}.\]
Also, we have the selling price of 10 mangoes as Rs. 11.
Here, we can see that the selling price is greater than the cost price, i.e. \[11>\dfrac{100}{11}.\]
So, we have a profit or gain. Now, we know that,
Gain = SP – Cost Price
\[=11-\dfrac{100}{11}\]
\[\Rightarrow \dfrac{121-100}{11}=Rs.\dfrac{21}{11}\]
\[\text{Gain Percent}=\dfrac{\text{Gain}}{CP}\times 100\]
\[\Rightarrow \dfrac{\dfrac{21}{11}}{\dfrac{100}{11}}\times 100\]
\[\Rightarrow \dfrac{21\times 11}{11\times 100}\times 100\]
= 21 %
So, we get the gain percent as 21 %.

So, the correct answer is “Option B”.

Note: Students should note that while finding the profit or loss, we should compare the same quantity. We were given 11 mangoes and 10 were sold. So one should always find the cost price of 10 mangoes. While solving the fraction, always remember \[\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\times d}{b\times c}.\] Slowly calculate and find the answer and always recheck when you have a complex calculation.