A pipe is cut into two pieces. The longer piece is 70% of the original length. By what percentage is the longer piece longer than the shorter piece?

Introduction / Context: The question asks for a relative comparison: how much longer the longer piece is compared to the shorter piece, expressed as a percentage of the shorter piece.

Given Data / Assumptions:

• Total length = L.
• Longer piece = 70% of L = 0.70L.
• Shorter piece = 30% of L = 0.30L.

Concept / Approach: Percentage by which A exceeds B is (A − B)/B * 100%. Substitute A = 0.70L and B = 0.30L and simplify; L cancels out.

Step-by-Step Solution:

Verification / Alternative check: Let L = 100 units: longer 70, shorter 30. Excess = 40 over base 30 = 133 1/3%.

Why Other Options Are Wrong: 40% uses the total length as the base; 140% and 133 1/3% are close but only 400/3% exactly represents 133 1/3% in fractional form as given in options.

Common Pitfalls: Using the total length as denominator instead of the shorter piece, which changes the base and hence the percentage.

Final Answer: 400/3%