Profit and Loss — Find the Cost Price (CP) when the Selling Price (SP) is ₹ 400 and the transaction incurs a 70% loss. Clearly state the relation SP = (1 − loss%) * CP and compute CP accordingly. Provide your final CP in exact fractional form as well as decimal form for clarity.

Introduction / Context: This problem tests the core relationship between Cost Price (CP), Selling Price (SP), and loss percentage in profit-and-loss. When there is a loss, SP is less than CP by the stated percentage. Understanding and applying the direct formula is sufficient to solve such questions quickly.

Given Data / Assumptions:

• SP = ₹ 400
• Loss% = 70%
• Standard relation for loss: SP = (1 − loss%) * CP

Concept / Approach: For loss p%, SP = (1 − p/100) * CP. Rearranging gives CP = SP / (1 − p/100). Substitute the known values to compute CP. Express the answer in exact fractional form and a decimal approximation for completeness.

Step-by-Step Solution:

Verification / Alternative check: If CP = 4000/3, then 70% of CP = 0.70 * (4000/3) = 2800/3, so SP = CP − loss = (4000/3) − (2800/3) = 1200/3 = 400, which matches the given SP.

Why Other Options Are Wrong: ₹ 5000/3, ₹ 2000/3, and ₹ 7000/3 do not satisfy SP = 30% of CP. ₹ 1333.33 is only a rounded decimal; the exact required form is ₹ 4000/3.

Common Pitfalls: A frequent mistake is doing CP = SP * (1 − loss%), which is incorrect. Always divide SP by (1 − loss%) to retrieve CP when loss is given on CP.

Final Answer: ₹ 4000/3