Question

A student purchased a computer system and a colour printer. If he sold the computer system at 10 loss and the colour printer at 20 gain, he would not lose anything. But if he sells the computer system at 5 gain and the colour printer at 15 loss, he would lose Rs. 800 in the bargain. How much did he pay for the colour printer?

• A. Rs. 8,000
• B. Rs. 16,000
• C. Rs. 9,000
• D. Rs. 5,334

Hint:

When solving percentage-based cost and selling price problems, use the relationships between the costs and percentages carefully to form equations.

Answer 1

The Correct Option is B

Let \( C \) and \( P \) be the cost price of the computer system and the printer respectively. \[ \text{Selling Price of Computer and Printer in Case I: } \text{SP} = 0.9C + 1.2P \] Since he did not lose anything: \[ C + P = 0.9C + 1.2P \quad \Rightarrow \quad C = 2P \] Now, Case II: \[ \text{Selling Price in Case II: } \text{SP} = 1.05C + 0.85P \] Given that there was a loss of Rs. 800: \[ \text{Loss} = C + P - 1.05C - 0.85P = 800 \] \[ \Rightarrow 800 = C + P - 1.05C - 0.85P = 0.15C + 0.15P \] Substitute \( C = 2P \) into the equation: \[ 800 = 0.15(2P) + 0.15P = 0.45P \] \[ P = \frac{800}{0.45} = 1777.77 \] So, the cost price of the printer is Rs. 16,000.