Let's solve this problem step by step.

1. Let the total work be denoted as $W$.

2. The rate of work done by A and B together is $\frac{1}{40}$ of the total work per day. This is because they can complete the whole work in 40 days.

   Therefore, A and B together complete $\frac{W}{40}$ of the work per day.

3. Let the rate of work done by A alone be $\frac{1}{A}$ of the work per day, and the rate of work done by B alone be $\frac{1}{B}$ of the work per day.

From the first condition:

• A works for 24 days. During this time, A and B together would have completed $24 \times \frac{W}{40} = \frac{24W}{40} = \frac{3W}{5}$ of the total work.

So, after 24 days, $1 - \frac{3W}{5} = \frac{2W}{5}$ of the work remains.

4. According to the second condition, B alone completes the remaining $\frac{2W}{5}$ of the work in 54 days.

Thus, the rate at which B works is $\frac{\frac{2W}{5}}{54} = \frac{2W}{5 \times 54} = \frac{W}{135}$ of the work per day.

5. Now, we know that B completes $\frac{W}{135}$ of the work in one day. Therefore, B alone can complete the entire work in 135 days.

Thus, B alone can complete the whole work in 135 days.

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Let me know if you'd like further details or clarifications!

Related Questions:

1. If A worked alone, how many days would it take for A to complete the work?
2. If A and B work together for 20 days and then B works alone, how many more days would B need to finish the work?
3. If A worked for 30 days and B worked for 40 days, what fraction of the work would be completed?
4. If A can finish the work in 60 days, how many days will it take for A and B together to finish the work?
5. How much more efficient is B compared to A based on their individual working days?

Tip:

In such work-rate problems, converting everything into rates of work per day and then using fractions is the most straightforward approach!