Deepak sells his smartphone at a price that results in a loss of 10%. He notices that if he had sold the same smartphone for Rs. 50 more, he would have made a profit of 5% instead. The initial loss amount is what percentage of the profit he would have earned at 5% profit?

Introduction / Context:
This question explores the relationship between profit and loss on the same item when the selling price changes. Deepak sells a smartphone at a loss, but a slightly higher selling price would turn that loss into a profit. We are asked to compare the original loss amount with the profit amount he would have earned, expressed as a percentage. It is a typical percentage-based profit and loss problem that requires setting up an equation with cost price and selling prices.

Given Data / Assumptions:

• At the actual selling price, there is a loss of 10%.
• If the selling price were Rs. 50 more, the profit would be 5%.
• Let the cost price (CP) of the smartphone be x rupees.
• We must find (loss amount / profit amount) * 100, expressed as a percentage.

Concept / Approach:
We express both the loss scenario and the hypothetical profit scenario using the same cost price x. For a 10% loss, selling price is 0.90x. For a 5% profit, selling price is 1.05x. The question states that increasing the selling price by Rs. 50 changes the situation from a 10% loss to a 5% profit. This yields an equation linking x and 50. Once x is found, we compute the loss and profit amounts and then find their ratio as a percentage.

Step-by-Step Solution:
Let the cost price of the smartphone be x rupees. At 10% loss, selling price SP1 = 0.90x. If sold for Rs. 50 more, new selling price SP2 = SP1 + 50 = 0.90x + 50. This new selling price corresponds to 5% profit, so SP2 = 1.05x. Equate the two expressions for SP2: 0.90x + 50 = 1.05x. Rearrange: 50 = 1.05x − 0.90x = 0.15x. Therefore, x = 50 / 0.15 = 333.33 (approximate). Loss amount at SP1 = 10% of x = 0.10x. Profit amount at SP2 = 5% of x = 0.05x. Now compute the ratio: loss / profit = 0.10x / 0.05x = 2. Expressed as a percentage: 2 * 100% = 200%.

Verification / Alternative check:
Take x = Rs. 333.33 approximately. Then SP1 at 10% loss is 0.90 * 333.33 ≈ Rs. 300. SP2 at 5% profit is 1.05 * 333.33 ≈ Rs. 350. The difference between SP2 and SP1 is about Rs. 50, which matches the given information. Loss amount is about Rs. 33.33 and profit amount is about Rs. 16.67. The ratio 33.33 / 16.67 is approximately 2, or 200%.

Why Other Options Are Wrong:
100%: This would mean the loss equals the profit, which contradicts our ratio of 2:1.
75% and 85%: These suggest the loss is smaller than the profit, which does not fit the algebraic relationship derived from the given prices.
150%: This is closer but still not equal to the exact ratio of 2:1 (200%).

Common Pitfalls:
Learners may confuse loss percentage and profit percentage and think that the difference of 15% directly gives the ratio. Another common error is to forget that the Rs. 50 difference is between two selling prices, not between cost price and selling price. Always explicitly express both selling prices in terms of cost price, equate them using the problem condition and then compare the actual loss and profit amounts.

Final Answer:
The initial loss is 200% of the profit that would have been earned at 5% profit.