Let's break down the problem step-by-step.

1. Given that $a$ is 40% less than $b$:

   This means: $a = b - 0.4b = 0.6b$

2. Given that $c$ is 40% of the sum of $a$ and $b$:

   The sum of $a$ and $b$ is: $a + b = 0.6b + b = 1.6b$

   Therefore: $c = 0.4 \times 1.6b = 0.64b$

3. Now, we need to find by what percent $b$ is greater than $c$:

   To find the percentage by which $b$ is greater than $c$, we use the formula: $\text{Percentage increase} = \frac{b - c}{c} \times 100$

   Substituting $c = 0.64b$: $\frac{b - 0.64b}{0.64b} \times 100 = \frac{0.36b}{0.64b} \times 100 = \frac{0.36}{0.64} \times 100$

   Simplifying: $\frac{0.36}{0.64} \approx 0.5625 \times 100 = 56.25\%$

Thus, $b$ is approximately 56.25% greater than $c$.

Would you like further details or have any other questions?

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Here are five related questions for further exploration:

1. If $a$ is instead 30% less than $b$, how would this affect the percentage by which $b$ is greater than $c$?
2. How would the result change if $c$ were 50% of the sum of $a$ and $b$ instead of 40%?
3. Can we generalize this problem to find the percentage difference for any $x\%$ reduction and any $y\%$ of the sum?
4. What happens if $a$ is equal to $b$ (i.e., no reduction)?
5. How would the result change if $c$ was defined as the product of $a$ and $b$ rather than a percentage of their sum?

Tip: When comparing two values, remember that the percentage increase or decrease depends on the reference point—always clarify which value is the baseline.