Price grid puzzle — A shoe brand's cost price (CP) and selling price (SP) must each be a multiple of one of 13, 14, 15, 16, 17, 18, or 19, and each price must lie between ₹ 399 and ₹ 699 inclusive. What is the maximum possible profit (SP − CP) under these rules?

Introduction / Context:
This is a discrete optimization over a constrained price grid. Both CP and SP must be multiples of one of the given integers and lie within a fixed rupee range. To maximize profit, pick the smallest valid CP and the largest valid SP subject to the constraints.

Given Data / Assumptions:

• Valid multipliers: 13, 14, 15, 16, 17, 18, 19.
• CP, SP ∈ [₹ 399, ₹ 699], each being an integer multiple of some listed multiplier (not necessarily the same one).
• Profit = SP − CP; maximize this difference.

Concept / Approach:
Compute the smallest valid multiple ≥ 399 and the largest valid multiple ≤ 699 for the allowed multipliers. The best pair usually takes the global minimum CP and global maximum SP from the feasible set.

Step-by-Step Solution:

Verification / Alternative check:
Both 399 and 697 satisfy the divisor rules and the range. No higher SP (within list) exceeds 697, and no lower CP (within list) is below 399.

Why Other Options Are Wrong:
₹ 300 and ₹ 398 exceed the feasible difference; ₹ 292 and ₹ 256 correspond to suboptimal pairs under the constraints.

Common Pitfalls:
Requiring CP and SP to use the same base multiple or forgetting to check the inclusive bounds (399 and 699 are allowed).

Final Answer:
Rs. 298