Two numbers are 30% and 37% less than a third number T. By what percent is the second number less than the first?

Introduction / Context:
Comparing two numbers that are each reduced from the same base is a common percent-comparison task. The trick is to express both numbers in terms of the shared base, then compute the relative difference with the correct denominator (the “first” number as the reference).

Given Data / Assumptions:

• Third number = T (baseline).
• First number = 30% less than T ⇒ 0.70T.
• Second number = 37% less than T ⇒ 0.63T.

Concept / Approach:
Percent by which the second is less than the first = (First − Second) / First * 100%. Substitute the expressions 0.70T and 0.63T and simplify; T cancels.

Step-by-Step Solution:

Verification / Alternative check:
Choose T = 100 arbitrarily: numbers become 70 and 63; difference 7 is 10% of 70. Check passes.

Why Other Options Are Wrong:
3% or 4% come from dividing by T instead of the first; 7% uses the absolute gap relative to 100; 11% is a rounding guess.

Common Pitfalls:
Using the wrong base when converting a difference to a percent. The phrase “less than the first” means divide by the first number.

Final Answer:
10%