Consider a three-digit number with hundreds digit h, tens digit t, and units digit u. The conditions are: u = 4h; after swapping the tens and units digits the new number is 18 greater than the original; and h is one-third of t. Find 25% of the original number.

Introduction / Context:
This digit puzzle combines ratio constraints on digits with a transformation (interchanging tens and units) that increases the number by a fixed amount. By expressing the number symbolically and applying the constraints, you can isolate each digit and then compute the requested fraction of the original number.

Given Data / Assumptions:

• Original number = 100h + 10t + u.
• u = 4h.
• t = 3h (since h is one-third of t).
• Swapping tens and units gives 100h + 10u + t, which is 18 more than original.
• Digits must be integers within 0–9, and h ≥ 1 for a three-digit number.

Concept / Approach:
Substitute t and u in terms of h to express both the original and swapped numbers. The difference equation will involve only h. Solve for h respecting digit bounds, then rebuild the number and compute 25% (one-quarter) of it.

Step-by-Step Solution:

Verification / Alternative check:
Swap tens and units: 268 → 286. Difference 286 − 268 = 18 (matches). Digit constraints u = 4h and t = 3h also hold, confirming correctness.

Why Other Options Are Wrong:
84, 96, and 137 do not equal one-quarter of 268. “Couldn’t not be determined” is incorrect because the constraints uniquely determine the number.

Common Pitfalls:
Misinterpreting “one-third” (taking t = h/3 instead of t = 3h), or forgetting to apply the swap correctly when forming the new number.

Final Answer:
67