Changing cost and price together: A man sells an article at a profit of 40%. If instead he had bought it at 40% less (than the original cost) and sold it for ₹ 5 less than his original selling price, he would have gained 50%. Find the original cost price.

Introduction / Context:
This problem links two scenarios through the same original selling price (minus ₹ 5) and a changed cost. Setting up an equation between the alternative selling price and the required 50% gain on the reduced cost yields the original CP.

Given Data / Assumptions:

• Original SP = 1.40 * C (40% profit on original cost C).
• Alternative cost = 0.60 * C (40% less).
• Alternative SP = (original SP) − ₹ 5, and at this price the gain would be 50% on the reduced cost.

Concept / Approach:
Equation: (1.40C − 5) = 1.50 * (0.60C) = 0.90C. Solve for C.

Step-by-Step Solution:
1.40C − 5 = 0.90C0.50C = 5C = ₹ 10

Verification / Alternative check:
Original SP = 1.40 * 10 = ₹ 14. Alternative SP = 14 − 5 = ₹ 9. Reduced cost = 0.60 * 10 = ₹ 6. Profit at ₹ 9 is ₹ 3, which is 50% of ₹ 6—verified.

Why Other Options Are Wrong:

• ₹ 15 / ₹ 20 / ₹ 30: do not satisfy the equation 1.40C − 5 = 0.90C.

Common Pitfalls:

• Applying 50% to the original cost instead of to the reduced cost.

Final Answer:
₹ 10