Profit and Loss – From 15% loss to 15% profit band (range check): A person sells an article for ₹ 136 at a 15% loss. If he had sold it for ₹ N, he would have gained 15%. Which interval correctly contains N?

Introduction / Context:
This is a two-scenario profit–loss conversion. The first selling price yields a 15% loss; the second (unknown) would yield a 15% profit. If we compute the cost price from the loss case, the profit case price is simply 15% higher than that cost price. The final step is to place N in the correct numerical interval.

Given Data / Assumptions:

• SP_loss = ₹ 136 at 15% loss
• SP_gain = ₹ N at 15% profit

Concept / Approach:
Let CP = x. With 15% loss, 0.85x = 136 ⇒ x = 136 / 0.85. Then N = 1.15x. Convert to a decimal value and determine the interval.

Step-by-Step Solution:
CP = 136 / 0.85 = 160N = 1.15 * 160 = 184Therefore, 180 < N < 190

Verification / Alternative check:
Check both directions: 15% loss from 160 gives 136; 15% profit gives 184, consistent with the stated conditions.

Why Other Options Are Wrong:
The ranges 170–180 and 160–170 are too low; 190–200 and above are too high.

Common Pitfalls:
Adding 15% to the loss price instead of using CP as the base.

Final Answer:
180 < N < 190