If A's income is 40% less than B's income, approximately by what percentage is…

Concept

When one quantity is stated as a percentage less than another, the comparison base changes when the direction is reversed.

If A is r% less than B, then A = (1 - r/100)B, and B's percentage excess over A is ((B - A)/A) × 100.

Application

1. Let B's income be 100 units.

2. A's income is 40% less, so A = 100 - 40 = 60 units.

3. B exceeds A by 100 - 60 = 40 units.

4. Use A as the base: (40/60) × 100 = 200/3 = 66⅔%.

5. The exact value is 66.666…%; among the given values, 66.66 is its truncated two-decimal representation.

Cross-check

1. Increasing 60 by the exact 66⅔% adds 40, so the total returns to 100.

2. Using the offered 66.66% adds 39.996 to 60, giving 99.996, which is effectively 100 at the options' stated precision.

3. Therefore, among the choices, B's income is approximately 66.66% more than A's income.