Question

When a pen is sold at a discount of 15%, there is a gain of Rs 10. But if it is sold at a 25% discount, there is a loss of Rs 2. Find the marked price of the pen.

(a) Rs 60
(b) Rs 80
(c) Rs 100
(d) Rs 120

Answer 1

The correct answer is option (c) Rs 100. To solve the problem, let's denote the marked price as MP. When the pen is sold at a 15% discount, the selling price is 0.85MP and there is a gain of Rs 10.

Step-by-step explanation:

Conversely, when the pen is sold at a 25% discount, the selling price is 0.75MP and there is a loss of Rs 2. We can set up two equations based on the information provided:

• 0.85MP - Cost Price (CP) = Rs 10 (gain)
• 0.75MP - CP = -Rs 2 (loss)

Solving these two equations, we first express CP in terms of MP using the first equation:

CP = 0.85MP - 10

Then we substitute CP from the first equation into the second:

0.75MP - (0.85MP - 10) = -2

This simplifies to:

0.75MP - 0.85MP + 10 = -2

-0.10MP = -12

MP = Rs 120

But upon closer inspection, it appears we have made an error in calculation. Let's try once more to correctly solve for MP:

0.75MP - (0.85MP - 10) = -2

-0.10MP + 10 = -2

MP = 120

Thus, even with the recalculation, we can see that the marked price ends up being Rs 120.