Question

The profit earned after selling an article for Rupees 996 is the same as the loss incurred after selling the article for Rupees 894. What is the cost price of the article?

• A. Rupees 935
• B. Rupees 905
• C. Rupees 945
• D. Rupees 975

Hint:

When equal profit and loss are mentioned at two selling prices, the cost price is simply the midpoint of those prices: \(C=\frac{SP_1+SP_2}{2}\).

Answer 1

The Correct Option is C

Step 1: Set up the equation.
Let cost price be \(C\). 
Profit at Rupees 996 \(=996-C\). 
Loss at Rupees 894 \(=C-894\). 
Given equal: \(996-C=C-894\). 

Step 2: Solve for \(C\).
\[ 996+894=2C \Rightarrow 1890=2C \Rightarrow C=945. \] \[ \boxed{Rupees \;945} \]

Answer 2

There is a well-known shortcut for this type of question: when the profit made at one selling price equals the loss made at another, the cost price is simply the average of the two selling prices.

1. Rupees 935: Profit at 996 would be \(996-935=61\) and loss at 894 would be \(935-894=41\). These are not equal, so this cost price is inconsistent.
2. Rupees 905: Profit would be \(996-905=91\) and loss would be \(905-894=11\). These are far from equal, so this fails too.
3. Rupees 945: Profit would be \(996-945=51\) and loss would be \(945-894=51\). These are exactly equal, satisfying the condition given in the question.
4. Rupees 975: Profit would be \(996-975=21\) and loss would be \(975-894=81\). These are not equal, so this is inconsistent.

Since profit at Rupees 996 equals loss at Rupees 894, the cost price is the average of these two selling prices: \(\dfrac{996+894}{2}=\dfrac{1890}{2}=945\).

So the correct answer is Rupees 945.