If A and B work together can complete a work in 8/5 days. A started th...
Given:
A and B together can complete a work in 8/5 days.
A completed 50% of the work alone and left the work.
B completed the remaining work in 5 days.
To find:
In how many days B can complete the work alone if A is more efficient than B?
Solution:
Let's assume that A is more efficient than B, so A's work capacity is more than B's work capacity.
Let's assume that the total work is 10 units to make calculations easier.
Step 1: Calculate A and B's work capacity
Let A's work capacity be x units per day.
Then B's work capacity will be (8/5 - x) units per day (as A and B together can complete the work in 8/5 days).
Step 2: Calculate the work done by A
A completed 50% of the work alone, which is 5 units (as the total work is assumed to be 10 units).
Step 3: Calculate the work done by B
B completed the remaining 5 units of work in 5 days.
So, B's work capacity is 1 unit per day (as B completed 5 units of work in 5 days).
Step 4: Calculate A's work capacity
We know that A completed 5 units of work in a certain number of days.
Let A's work capacity be x units per day.
So, the number of days A took to complete 5 units of work will be 5/x.
We also know that A completed 50% of the work alone, which is 5 units.
So, the total work is 10 units.
Therefore, A completed 5 units in 5/x days and B completed 5 units in 5 days.
So, the total time taken to complete 10 units of work will be:
5/x + 5 = 8/5
Solving the above equation, we get:
x = 4 units per day
Step 5: Calculate B's work capacity
We know that A's work capacity is x units per day and B and A together can complete the work in 8/5 days.
So, B's work capacity will be (8/5 - x) units per day.
Substituting x = 4, we get:
B's work capacity = (8/5 - 4) = 0.4 units per day.
Step 6: Calculate the time taken by B to complete the work alone
We know that B's work capacity is 0.4 units per day and the total work is 10 units.
So, B will take 25 days to complete the work alone.
Therefore, the correct option is (d) 4 days.
If A and B work together can complete a work in 8/5 days. A started th...
D) 4 Days