A is 40 % more efficient than B and both work together can complete a work in 9 3/8 days. If A work for first five days alone and remaining work complete by B, then find in how many days total work will be completed?

Let the amount of work done by A and B together be considered as 1 unit.

### Step 1: Define the work rates
Assume B's efficiency (rate of work) is \( x \) units of work per day. Since A is 40% more efficient than B, A's efficiency will be:

\[
A's\ efficiency = x + 0.4x = 1.4x
\]

### Step 2: Work done together
If A and B together can complete the entire work in \( 9 \frac{3}{8} \) days, we first convert this into an improper fraction:

\[
9 \frac{3}{8} = \frac{75}{8} \text{ days}
\]

Since their combined efficiency is \( 1.4x + x = 2.4x \), the total work they can complete in one day is \( 2.4x \). Thus, the total work equation can be written as:

\[
2.4x \times \frac{75}{8} = 1
\]

Simplifying this equation:

\[
2.4x \times 9.375 = 1
\]

\[
x = \frac{1}{2.4 \times 9.375} = \frac{1}{22.5} = 0.04444
\]

Thus, B’s efficiency \( x = 0.04444 \) units of work per day, and A’s efficiency is:

\[
A's\ efficiency = 1.4 \times 0.04444 = 0.06222
\]

### Step 3: Work done by A in the first 5 days
If A works alone for 5 days, the work done by A in those 5 days is:

\[
\text{Work done by A in 5 days} = 0.06222 \times 5 = 0.3111
\]

This means A completes 31.11% of the total work in the first 5 days.

### Step 4: Remaining work done by B
The remaining work is:

\[
1 - 0.3111 = 0.6889
\]

Now, B completes this remaining work alone. Since B’s efficiency is \( 0.04444 \), the time required for B to complete the remaining work is:

\[
\text{Time for B} = \frac{0.6889}{0.04444} = 15.5 \text{ days}
\]

### Step 5: Total time
The total time taken to complete the work is:

\[
5 \text{ days} + 15.5 \text{ days} = 20.5 \text{ days}
\]

Thus, the total time required to complete the work is **20.5 days**.

---

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to explore further:
1. What if A was 50% more efficient than B instead?
2. How would the time change if B worked the first 5 days instead of A?
3. How is the total work distributed if A and B work for an equal number of days?
4. How would the answer change if they worked at different times but not continuously?
5. How would the calculation change if a third worker with half B's efficiency joined?

**Tip**: Always convert mixed fractions into improper fractions for easier calculations!

A is 40% more efficient than B and both work together can complete a work in 9 3/8 days. If A works for the first five days alone and the remaining work is completed by B, then find in how many days the total work will be completed.

Explore how to calculate the time needed to complete a task with two workers of different efficiencies. Given A is 40% more efficient than B, find the total days required when A starts alone for the first 5 days, followed by B. This solution covers efficiency, work rates, and step-by-step fraction conversions.

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