A photographer allows a 10% discount on the advertised marked price of a camera. If the camera costs him Rs 600 and he wants to earn a profit of 20% on his cost price, what marked price (in Rs) should he print on the camera so that after the discount he still gets the desired profit?

Introduction / Context:
This question checks understanding of the relationship between cost price, marked price, discount and desired profit. It is a classic profit and loss situation where the seller offers a discount but still wants to achieve a specific profit percentage. Students must be able to work backwards from the required profit to the necessary marked price.

Given Data / Assumptions:

• Cost price of the camera = Rs 600.
• Desired profit = 20% on cost price.
• Discount allowed on marked price = 10%.
• We assume no taxes or additional charges.

Concept / Approach:
First, we compute the selling price needed to achieve a 20% profit on the cost price. Profit percent is always calculated on cost price unless stated otherwise. Then, since the camera will be sold after allowing a 10% discount on the marked price, we express selling price as 90% of the marked price. From this equation we can solve for the required marked price. Understanding that discount is applied on the marked price, not on cost price, is crucial.

Step-by-Step Solution:
Step 1: Cost price (CP) = Rs 600. Step 2: Desired profit = 20% of CP = 0.20 * 600 = Rs 120. Step 3: Required selling price (SP) = CP + profit = 600 + 120 = Rs 720. Step 4: Let the marked price be M. After a 10% discount, SP = 90% of M = 0.90 * M. Step 5: Set 0.90 * M = 720 and solve for M. Step 6: M = 720 / 0.90 = 800. Step 7: Therefore, the photographer must mark the camera at Rs 800.

Verification / Alternative check:
We can verify quickly: 10% of 800 is 80, so discounted price = 800 - 80 = 720. This is exactly the selling price that gives a 20% profit over the cost price of 600. Hence the marked price of Rs 800 is correct.

Why Other Options Are Wrong:

• 650: Even without discount, this price would give a profit of only 50 over 600, which is less than 20%.
• 700: After 10% discount, selling price would be 630, which is just 5% profit on 600.
• 850: After 10% discount, selling price would be 765, which is more than the required 20% profit.
• 900: After 10% discount, selling price becomes 810, far greater than the targeted profit margin.

Common Pitfalls:
A common mistake is to calculate the 20% profit on the marked price instead of the cost price. Another frequent error is to forget that the 10% discount is on the marked price and to subtract 10% from the cost price instead. Students also sometimes try to add or subtract percentages without translating them into actual amounts, which leads to incorrect results.

Final Answer:
The camera should be marked at Rs 800 so that, after a 10% discount, the photographer still earns a 20% profit on his cost price.