Price adjustment scenario — A shopkeeper sells a transistor at 15% above its cost. If instead he had bought it at 5% more than his original cost and also sold it for ₹ 6 more than his original selling price, he would have made 10% profit. What is the (original) cost price of the transistor?

Difficulty: Medium

Correct Answer: ₹ 1200

Explanation:


Introduction / Context:
This is a two-scenario price puzzle. In the real scenario, the seller gains 15% over cost. In a hypothetical scenario, both the cost and selling price are adjusted, resulting in a 10% profit. We form an equation in the unknown cost price and solve.


Given Data / Assumptions:

  • Let original cost = C; original selling price = 1.15C.
  • Alternate scenario: new cost = 1.05C; new selling price = 1.15C + ₹ 6.
  • Alternate profit = 10% ⇒ new SP = 1.10 * new cost.


Concept / Approach:
Set 1.15C + 6 = 1.10 * (1.05C) and solve for C. This linear equation gives the original cost price directly.


Step-by-Step Solution:

Equation: 1.15C + 6 = 1.10 * 1.05C = 1.155C.6 = 1.155C − 1.15C = 0.005C.C = 6 / 0.005 = ₹ 1200.


Verification / Alternative check:
Original SP = 1.15 * 1200 = ₹ 1380. Alternate: cost = 1260; SP = 1386 ⇒ profit = 126 ⇒ 10% of 1260, consistent.


Why Other Options Are Wrong:
₹ 800, ₹ 900, ₹ 1000, and ₹ 1400 do not satisfy the equation 1.15C + 6 = 1.155C.


Common Pitfalls:
Adding or subtracting the percentages instead of multiplying, or forgetting that the alternate 10% is on the new cost.


Final Answer:
₹ 1200

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