A is 4 times more efficient than B. A and B together complete a work in 20 days. In how many days B individually  will complete the same work?

Let the total amount of work be \( W \). Let the efficiency (work per day) of B be \( b \). Since A is 4 times more efficient than B, the efficiency of A is \( 4b \).

When A and B work together, their combined efficiency is:
\[
b + 4b = 5b
\]
It is given that together, A and B complete the work in 20 days. So, in 1 day, A and B together complete \( \frac{1}{20} \) of the total work:
\[
5b = \frac{1}{20}
\]
Solving for \( b \):
\[
b = \frac{1}{20 \times 5} = \frac{1}{100}
\]
Thus, B’s efficiency is \( \frac{1}{100} \), meaning B completes \( \frac{1}{100} \) of the work per day.

Therefore, B alone will complete the entire work in:
\[
\text{Number of days} = \frac{1}{\frac{1}{100}} = 100 \text{ days}
\]

So, B will complete the work in 100 days.

Would you like more details on any step?

Here are 5 related questions for practice:
1. If A completes the work alone, how many days will it take?
2. If B’s efficiency were doubled, how many days would A and B together take to complete the work?
3. How many days will it take if A works for 10 days alone, and then B completes the rest of the work?
4. If A and B together complete 50% of the work in 10 days, how many days would it take them to complete the remaining 50%?
5. What fraction of the total work is done by A in one day?

**Tip:** When dealing with work-related problems, always consider defining the total work as 1 unit for simplicity.

A is 4 times more efficient than B. A and B together complete a work in 20 days. In how many days B individually will complete the same work?

Solve a work and time problem where A is 4 times more efficient than B. Learn how A and B together complete a work in 20 days and calculate how many days B alone will take to finish the work. This step-by-step solution explains efficiency concepts and key formulas, ideal for students in Grades 8-10.

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