A’s	efficiency	is	twice	that	of	B's.	A	can	work	only	for	8	hours	a	day	while	B	can	work	for	12	hours	a	
day.	If	A	can	finish	a	work	in	12	days,	in	how	many	days	can	B	finish	the	same	work?

Let A's efficiency be \( 2x \) and B's efficiency be \( x \).

- A can finish the work in 12 days, working 8 hours per day.
- Total work done by A in 12 days is:

\[
\text{Total work} = \text{Efficiency} \times \text{Total hours} = 2x \times (12 \times 8) = 192x \text{ units}
\]

Now, let’s calculate the time B would take to complete the same work:

\[
\text{Total work} = 192x
\]

- B’s efficiency is \( x \).
- B works 12 hours a day. Let \( d \) be the number of days B takes to finish the work.

\[
\text{Total work} = \text{Efficiency} \times \text{Total hours} = x \times (12 \times d) = 12xd
\]

Setting both expressions for total work equal:

\[
192x = 12xd
\]

\[
192 = 12d
\]

\[
d = 16
\]

So, B can finish the same work in 16 days.

Would you like more details or have any questions? Here are some related questions:

1. How do you determine the efficiency of a worker?
2. What happens if both A and B work together?
3. How can we calculate work done if the efficiency varies over time?
4. What if A works more hours per day?
5. How does changing the number of hours worked per day affect completion time?

**Tip:** To solve work and efficiency problems, always define the efficiency in terms of work units per hour or day to simplify calculations.

A’s efficiency is twice that of B's. A can work only for 8 hours a day while B can work for 12 hours a day. If A can finish a work in 12 days, in how many days can B finish the same work?

Learn how to calculate the time B would take to finish a task when A’s efficiency is twice that of B's. This problem involves key work and time calculations, efficiency comparisons, and proportionality, making it ideal for Grades 9-10 students.

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