Question

A merchant buys 1260 kg of corn $\dfrac{1}{4}$of which he sells at a gain of 5%, $\dfrac{1}{3}$at a gain of 8% and the remainder at a gain of 12%. If he had sold the whole at a gain of 10%, he would have gained Rs 27.30 more. Find the cost price per kg.
A.Rs 5
B.Rs 2
C.Rs 3
D.Rs 2.50

Answer 1

Hint: Find the gain at which each portion of corn is sold and add all the gains of the portions of corn.
Now as per the question we know that this gain is less with Rs. 27.30 when the complete corn is sold at 10%. We create a linear equation with this condition and find the price of per Kg of corn.

Complete step-by-step answer:
We will assume cost price (CP) of corn per kg = Rs. x
Then, the total cost price of corn will be = Rs 1260x
Now if we are selling $\dfrac{1}{4}$th of the corn, then the merchant gain = 5%
\[ \Rightarrow Gain\;1 = \left( {1260x \times \dfrac{1}{4}} \right) \times \dfrac{5}{{100}} = Rs\;15.75x\;\]
Now if we are selling $\dfrac{1}{3}$th of the corn, then the merchant gain = 8%
\[ \Rightarrow Gain\;2 = \left( {1260x \times \dfrac{1}{3}} \right) \times \dfrac{8}{{100}} = Rs\;33.60x\;\]
Then at last for the remaining corn, the merchant gain = 12%
\[ \Rightarrow Gain\;3 = \left( {1260x - \left( {1260x \times \dfrac{1}{4}} \right) - \left( {1260x \times \dfrac{1}{3}} \right)} \right) \times \dfrac{{12}}{{100}} = Rs\;63.00x\;\]
Hence, Total gain = Gain 1 + Gain 2 +Gain 3
\[ \Rightarrow Total{\text{ }}gain{\text{ }} = {\text{ }}15.75x + 33.60x + 63.00x = 112.35x\]
 Now, according to the condition given in the question, if whole corn is sold then 10% gain is earned but this gain would be 27.30 more.
\[\; \Rightarrow 1260x \times \dfrac{{10}}{{100}} = Total\;Gain + 27.30\]
Substituting the value of total gain
\[\; \Rightarrow 126x = 112.35x + 27.30\]
Segregating all x terms on one side
\[\; \Rightarrow 126x - 112.35x = 27.30\]
\[\; \Rightarrow 13.65x = 27.30\]
Dividing the complete equation by 13.65
\[\; \Rightarrow x = \dfrac{{27.30}}{{13.65}} = 2\]
Hence the cost per kg of corn is = x = Rs 2.
So, option (B) is the correct answer.

Note: In this question, it is very important to understand the language of the question as some can get confused by it. Also remember that in the question, he gained profit in both the cases so we have to just equate the gain with the condition given in the question. In cases he suffered a loss in one case and gained in one then we have equated with the negative value of loss.