A can complete a piece of work in 20 days and B can complete the same work in 25 days. If both of them work together, what percentage of the total work will be completed in 3 days?

Introduction / Context:
This is a direct time and work percentage problem. We are given the individual times taken by A and B to finish a job alone and we must determine what fraction or percentage of the job they can finish together in a fixed short period of 3 days. This tests understanding of work rate addition and conversion of a fraction of work into a percentage.

Given Data / Assumptions:
- A can complete the entire work in 20 days. - B can complete the same work in 25 days. - A and B work together at their constant respective rates. - We are interested in the portion of work completed in exactly 3 days. - Total work is considered as one complete unit.

Concept / Approach:
If someone finishes a job in T days, their daily work rate is 1 / T of the job per day. When two workers collaborate, their joint rate is simply the sum of their individual rates. We calculate the combined daily rate of A and B, multiply it by 3 to find the fraction of work done in 3 days, and then convert this fraction into a percentage by multiplying by 100.

Step-by-Step Solution:
Step 1: A's daily work rate = 1 / 20 job per day. Step 2: B's daily work rate = 1 / 25 job per day. Step 3: Combined daily rate of A and B = 1 / 20 + 1 / 25. Step 4: Use a common denominator 100: 1 / 20 = 5 / 100 and 1 / 25 = 4 / 100, so sum = 9 / 100 job per day. Step 5: Work completed in 3 days = 3 * (9 / 100) = 27 / 100 of the job. Step 6: Convert fraction 27 / 100 to percentage: (27 / 100) * 100 percent = 27 percent.

Verification / Alternative check:
We can check if the answer is reasonable. A alone would do 3 * (1 / 20) = 3 / 20 = 15 percent of the job in 3 days. B alone would do 3 * (1 / 25) = 3 / 25 = 12 percent. Together, they should do 15 percent + 12 percent = 27 percent, which matches our detailed calculation. This quick mental check confirms that the answer is consistent.

Why Other Options Are Wrong:
9 or 12: These correspond roughly to the individual contributions of B or A alone, ignoring the fact that both work together.
25: This slightly underestimates the combined contribution; the precise fraction we computed is 27 / 100, not 25 / 100.
30: This overestimates the work done; for 30 percent, the combined daily rate would need to be higher than the given 9 / 100 job per day.

Common Pitfalls:
A common mistake is to average the times (20 and 25) rather than add the rates. Others may forget to convert the fraction to a percentage properly. Always remember that you add rates, not times, for workers cooperating, and then multiply the combined rate by the given number of days to get the fractional work done.

Final Answer:
A and B together will complete 27 percent of the work in 3 days.