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: In this question we have been given the cost price and selling price of the oranges which are in dozens quantities. Then we easily calculate the value of oranges in the cost price and selling price forms. Then convert the value of orange’s number again into dozens.

Complete step-by-step answer:
Let us assume that the number of arranges is x dozens in both purchases.
So, x dozens of oranges are purchased at Rs. $10$ per dozen cost. And x dozens of oranges are purchased at Rs. $10$ per dozen cost too.
Therefore, the total number of oranges purchased will be x+x $ = 2x$ dozens.
Now, we need to calculate cost price $2x$ dozens oranges, as bellow,
Cost at the rate of Rs. 10 + cost at the rate of Rs. 8
 $
   \Rightarrow 10x + 8x \\
   \Rightarrow 18x \\
$
Cost price = 18x
Also, selling price of total \[2x\]dozens at the rate of Rs. 11, will be
$ = 11 \times 2x = 22x$
Selling price = 22x
So, find the profit using the formula,
profit = Selling price – cost price
$ \Rightarrow $profit = 22x – 18x = 4x. …(1)
As, it is given in the question that profit should be Rs. 120.
So, in equation (1) , we have
4x = 120
$ \Rightarrow $ x = $\dfrac{{120}}{4}$
$ \Rightarrow x = 30$
Thus, total number of orange purchased $ = 2x$ = 2 $ \times $ 30 = 60
$\therefore $ The total number of oranges purchased is 60 dozens .Or $2 \times 30 = 60$ dozens of oranges.

Option D is the correct answer.

Note: The question is based on a very easy concept which is CP and SP price, we can calculate it by one another method that is an elementary method and can calculate profit on a single unit and then multiplied it no of term and find total terms.