Question

Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
1. Rs. 1200
2. Rs. 800
3. Rs. 1000
4. Rs. 500

Answer 1

Correct Answer - Option 4 : Rs. 500

Given:

Cost price(CP) of 8 pens and 4 pencils = Rs. 2400

Profit on pencils = 20%

Loss on pens = 10%

Overall profit = Rs. 240

Formula used:

Profit = SP - CP

Loss = CP - SP

Profit/Loss% = \(\dfrac{Profit / Loss}{CP} \times 100 \)

SP = Selling price

Calculation:

Let the CP of pens be x

Then, CP of pencils = 2400 - x

According to the question:

SP of pens = 0.9x

SP of pencils = 1.2(2400 - x) = 2880 - 1.2x

Overall SP = 2400 + 240 = 2640

Also, 0.9x + 2880 - 1.2x = 2640

⇒ 240 = 0.3x

⇒ x = 800

⇒ Cost of pens and pencils respectively = 800 and 1600

⇒ Cost of 1 pen = 800/8 = 100

⇒ Cost of 1 pencil = 1600/4 = 400

∴ Cost of 1 pen and 1 pencil = 400 + 100 = Rs. 500