Question

A man bought some oranges at Rs.10 per dozen and bought the same number of oranges at Rs.8 per dozen. He sold these oranges at Rs.11 per dozen and gained Rs.120. The total number of oranges he bought was:
A) 30 dozens
B) 40 dozens
C) 50 dozens
D) 60 dozens

Answer 1

Hint:
Here, we will assume the total number of oranges bought by the man at one time to be some variable. Then we will find the Cost Price and Selling Price of the oranges in terms of the assumed variable using the given information. We will then substitute the obtained values and given profit in the profit formula and simplify it further to find the total number of oranges bought by the man at one time. We will multiply the obtained number of oranges by 2 to get the required answer.

Formula Used:
\[{\rm{Profit}} = SP - CP\]

Complete step by step solution:
Let the total number of oranges bought by the man at one time be \[x\] dozen oranges.
According to the question, he bought some oranges at \[{\rm{Rs}}10\] per dozen and bought the same number of oranges at \[{\rm{Rs}}8\] per dozen.
Hence, the total number of oranges bought by him will be \[2x\] oranges.
So, the Cost Price of these oranges \[ = 10x + 8x = 18x\]
This is because it is given that the first \[x\] dozen oranges were bought for \[{\rm{Rs}}10\] per dozen and the next \[x\] dozen oranges were bought for \[{\rm{Rs}}8\] per dozen.
Now, it is given that he sold these oranges at \[{\rm{Rs}}11\] per dozen. Therefore,
The Selling Price of these \[2x\] dozen oranges \[ = 2x\left( {11} \right) = 22x\]
Now, substituting \[SP = 22x\], \[CP = 18x\] and \[{\rm{Profit}} = 120\] in this formula \[{\rm{Profit}} = SP - CP\], we get,
\[120 = 22x - 18x\]
Subtracting the like terms, weget
\[ \Rightarrow 120 = 4x\]
Dividing both sides by 4, we get
\[ \Rightarrow x = 30\]
We know that the man has bought \[2x\] oranges. Therefore,
The total number of oranges bought by him\[ = 2 \times 30 = 60\]
So, he bought 60 dozen oranges.

Hence, option D is the correct answer.

Note:
We know that the Cost Price is the amount at which the retailer/seller has bought the product. Selling Price is the amount at which the buyer/customer is willing to purchase that product. Now, if the Cost Price is greater than the Selling Price then there is a loss for the seller but if the Selling Price is greater than the Cost Price then there is a profit.
While solving this question, we should keep in mind that the man has bought \[2x\] oranges. This is because, after finding the value of \[x\], we could simply mark our answer as A and hence, make it wrong. These small mistakes can change our whole answer thus, we should be careful while solving such questions.