A trader sells a cycle at a loss of 10 percent. If he had increased the selling price by Rs. 200, he would have made a profit of 6 percent instead of a loss. What is the cost price of the cycle?

Introduction / Context:
This problem tests the core percentage profit and loss concept where the selling price is changed and we need to recover the original cost price. Such questions are very common in bank exams, SSC, railways and other aptitude tests, so understanding the structure of the equation is extremely useful.

Given Data / Assumptions:

• The trader first sells the cycle at a loss of 10 percent.
• If the selling price is increased by Rs. 200, there is a profit of 6 percent.
• We assume cost price is a positive real number.
• Market conditions, taxes and other charges are ignored.

Concept / Approach:
We express both selling prices in terms of the same unknown cost price. Loss of 10 percent means the selling price is 90 percent of cost price. Profit of 6 percent means the selling price is 106 percent of cost price. The difference between these two selling prices is given as Rs. 200. Solving this linear equation gives the cost price.

Step-by-Step Solution:
Let cost price = C.First selling price at 10 percent loss = 0.9 * C.New selling price at 6 percent profit = 1.06 * C.Difference between these selling prices = 1.06 * C - 0.9 * C = 0.16 * C.Given that this difference is Rs. 200, so 0.16 * C = 200.Therefore, C = 200 / 0.16 = 1250.

Verification / Alternative check:
If cost price is Rs. 1250, then 10 percent loss selling price is 0.9 * 1250 = 1125. At 6 percent profit, selling price is 1.06 * 1250 = 1325. The difference between 1325 and 1125 is exactly Rs. 200, so our computation is consistent with the conditions in the question.

Why Other Options Are Wrong:
Rs. 1200, Rs. 1205 and Rs. 1275 do not satisfy the equation 0.16 * C = 200. If you substitute any of these values, the difference between the two selling prices will not be exactly Rs. 200, so they cannot be correct cost prices.

Common Pitfalls:
Candidates often subtract percentage values directly or try to apply the difference 6 + 10 = 16 percent without linking it to the cost price. The key is to express both selling prices in terms of cost price and then equate their difference to the given rupee difference. Forgetting that loss and profit percentages are always on cost price is another frequent mistake.

Final Answer:
The cost price of the cycle is Rs. 1250.