A pole has 4/7 of its length buried in mud. After pulling out 1/3 of the total pole length, 250 cm still remains in the mud. Determine the full length of the pole (in cm).

Introduction / Context: This application problem practices fraction operations and interpreting changes relative to the total length, not just the buried portion.

Given Data / Assumptions:

• Initial buried length = (4/7) * L.
• Pulled out later = (1/3) * L (of the total length).
• Remaining buried length after pulling = 250 cm.

Concept / Approach: Compute the new buried portion as initial buried minus the length pulled out. Set that equal to 250 and solve for L. Carefully handle fractional subtraction with a common denominator.

Step-by-Step Solution:

Verification / Alternative check: Compute (4/7)*1050 = 600 cm initially buried; pulled out (1/3)*1050 = 350 cm; remaining buried = 600 - 350 = 250 cm, which matches the condition.

Why Other Options Are Wrong: 1000, 1100, 950 do not satisfy (5/21)L = 250 when checked; they yield 238.1, 261.9, or 226.2 cm respectively, not 250 cm.

Common Pitfalls: Misreading “1/3 of it” as one-third of the buried part rather than one-third of the total; arithmetic errors with fractions; forgetting to reduce to a common denominator for subtraction.

Final Answer: 1050