Profit and Loss — A cycle is sold for ₹ 2345 at a loss of 19%. Estimate the original Cost Price (CP) accurately by inverting the percentage-loss relation. Provide the nearest whole-rupee value as asked.

Introduction / Context: This question checks if you can reverse a loss-percentage situation to recover the Cost Price (CP) from a known Selling Price (SP) when there is a stated loss. The final answer is requested as a near (approximate) value.

Given Data / Assumptions:

• SP = ₹ 2345
• Loss% = 19%
• Loss is on CP (standard convention)
• Answer required: nearest CP

Concept / Approach: For a loss of p%, SP = (1 − p/100) * CP. Hence CP = SP / (1 − p/100). We compute the exact value and then round to the nearest option as required.

Step-by-Step Solution:

Verification / Alternative check: If CP ≈ ₹ 2895, then loss 19% ≈ 0.19 * 2895 ≈ ₹ 550. Hence SP ≈ 2895 − 550 ≈ ₹ 2345, confirming consistency. Since exact option ₹ 2895/₹ 2900 is not present, choose the nearest option ₹ 3000 as per the problem’s instruction “nearly”.

Why Other Options Are Wrong: ₹ 4000, ₹ 5000, and ₹ 3500 would imply SP values far from ₹ 2345 at 19% loss. ₹ 2900 is closer numerically but not listed as the accepted nearest in this set; per the given choices and typical instructions, ₹ 3000 is selected as the closest among provided options.

Common Pitfalls: Confusing “nearest” with exact computation, or reversing the multiplier (multiplying by 0.81 instead of dividing) which would understate CP.

Final Answer: ₹ 3000