Working 5 hours a day. A can' complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in

Options

A. 3 days
B. 4 days
C. 4.5 days
D. 5.4 days

Answer

To solve the problem step by step, we will first determine the total amount of work done by A and B individually, and then find out how long they take to complete the work together when working 8 hours a day.

### Step 1: Calculate the total work done by A
A works for 5 hours a day and can complete the work in 8 days.
- Total work done by A = hours worked per day × number of days
- Total work done by A = 5 hours/day × 8 days = 40 hours

### Step 2: Calculate the total work done by B
B works for 6 hours a day and can complete the work in 10 days.
- Total work done by B = hours worked per day × number of days
- Total work done by B = 6 hours/day × 10 days = 60 hours

### Step 3: Calculate the work rate of A and B
The work rate is the fraction of work completed in one hour.
- Work rate of A = 1/Total work done by A = 1/40
- Work rate of B = 1/Total work done by B = 1/60

### Step 4: Calculate the combined work rate of A and B
To find the combined work rate when A and B work together, we add their individual work rates:
- Combined work rate = Work rate of A + Work rate of B
- Combined work rate = 1/40 + 1/60

To add these fractions, we need a common denominator. The least common multiple (LCM) of 40 and 60 is 120.
- 1/40 = 3/120
- 1/60 = 2/120
- Combined work rate = 3/120 + 2/120 = 5/120 = 1/24

### Step 5: Calculate the time taken to complete the work together
If A and B can complete 1/24 of the work in one hour, then the total time taken to complete the entire work is the reciprocal of their combined work rate:
- Time taken = 1 / (1/24) = 24 hours

### Step 6: Calculate the time taken when working 8 hours a day
Now, we need to determine how many days it will take them to complete the work if they work 8 hours a day:
- Total hours needed = 24 hours
- Days needed = Total hours needed / hours worked per day
- Days needed = 24 hours / 8 hours/day = 3 days

### Final Answer
Therefore, working together for 8 hours a day, A and B can complete the work in **3 days**.