Question

Mr. A purchased two pens for Rs 1000. He sells one at 10% profit and other at 15% loss. Then, he neither loss nor gain.find the cost price of each pen.
1. Rs. 500, and Rs. 500
2. Rs. 600 and Rs. 400
3. Rs. 700 and Rs. 300
4. Rs. 200 and Rs. 800

Answer 1

Correct Answer - Option 2 : Rs. 600 and Rs. 400

Given

Cost price of two pens = Rs. 1000

Formula used

Selling Price = Cost price + Profit

Or

Selling price = Cost price - loss

Calculation

Let the cost price of one pen is Rs. x and other per is Rs. (1000 - x)

Selling price = x + 10% of x

⇒ 110x/100

Selling price = (1000 - x ) - 15% of (1000 - x)

⇒ (1000 - x) - [15(1000 - x)/100]

⇒ (100000 - 100x - 15000 + 15x)/100

⇒ (85,000 - 85x)/100

There is no loss or profit on selling of pens, therefore cost price is equal to selling price 

(85000 - 85x)/100 + 110x/100 = 1000

⇒ 85000 + 25x = 100000

⇒ 25x = 15000

⇒ x = 600

Second 1000 - 600

⇒ Rs. 400

∴ Cost price of pen is Rs. 600 and Rs. 400