Question

If by selling 110 mangoes, the C.P. of 120 mangoes is realised. Then the gain percent is?
(a). \[9\dfrac{1}{11}%\]

(b). \[9\dfrac{1}{9}%\]
(c). \[10\dfrac{10}{11}%\]
(d). \[11\dfrac{1}{9}%\]

Answer 1

- Hint: We will solve this question by computing the Cost price (CP) of one mango and proceed the question using the formula \[P%=\dfrac{\operatorname{Profit}}{CP}100\], where P% is the profit percent attained.

Complete step-by-step solution -

Here CP denotes Cost price, SP denotes Selling Price, P is the profit earned in the above transaction and P% is the profit percent.
Let the cp of one mango be Rs 1.
Then the CP of 110 mangoes can be obtained by multiplying 1 to 110.
Therefore, the CP of 110 mangoes will be = 1 x 110.
Now it is been given that SP of 110 mangoes is equal to CP of 120 mangoes,
Hence, CP of 120 mangoes will be = 1 x 120.
So, the CP of 120 mangoes will be = Rs 120.
Therefore, according to the given condition of the question we have,
The SP of 110 mangoes is = Rs 110.
So, the profit is = SP – CP = 120 -110 = 10.
Therefore, the profit is Rs.10.
Using the formula given as \[P%=\dfrac{\operatorname{Profit}}{CP}100\], where P% is the profit percent attained.
Therefore, the Profit Percent will be,
Substituting the values of CP and profit in the above equation, we get,
$ \Rightarrow P%=\dfrac{10}{110}100
  \Rightarrow P%=9\dfrac{1}{11}% $
Hence, the profit percent in the above transaction is \[9\dfrac{1}{11}%\] i.e. option (a).

Note: The possibility of error in these types of questions can be not equating the number of mangoes for which CP and SP are the same. We need to take care of the quantities of mangoes used in various steps in solving the question, so as to obtain the correct solution.