If A and B work together can complete a work in 8/5 days. A started th...
Given:
A and B can complete a work in 8/5 days when they work together.
A completed 50% of the work and left.
B completed the remaining work in 5 days.
A is more efficient than B.
To find:
In how many days B can complete the work alone.
Solution:
Let's assume that the total work to be completed is 10 units (just for simplicity).
Step 1: Finding the work efficiency of A and B
Let's assume that A completes x units of work in one day.
Then, B completes (10-x) units of work in one day.
As per the given condition, A and B can complete the work in 8/5 days.
Hence, the total work done by A and B in one day = 10/(8/5) = 6.25 units.
Therefore, we can write the following equation:
x + (10-x) = 6.25
Solving the above equation, we get:
x = 3.125 (work efficiency of A)
10-x = 6.875 (work efficiency of B)
Step 2: Work done by A and B
As per the given condition, A completed 50% of the work.
Hence, the work done by A = 5 units.
Therefore, the remaining work = 10-5 = 5 units.
Now, B completed the remaining work in 5 days.
Hence, the work done by B in one day = 1 unit.
Step 3: Finding the time taken by B to complete the work alone
Let's assume that the time taken by B to complete the work alone is t days.
Then, the work done by B in one day = 1/t units.
As per the given condition, B's work efficiency = 6.875 units per day.
Therefore, we can write the following equation:
6.875 = 1/t
Solving the above equation, we get:
t = 1.45 days or approximately 1 day and 11 hours.
Answer:
Hence, B can complete the work alone in approximately 1 day and 11 hours if A is more efficient than B.
If A and B work together can complete a work in 8/5 days. A started th...
Let A complete 50%(=1/2) of work in x days.
then B will complete 50%(=1/2) of work in (5-x) days.
part of work completed by A in 1 day = 1/2 ÷ x= 1/2x
part of work completed by B in 1 day = 1/2 ÷ (5-x) = 1/2(5-x)
part of work done by A and B in 1 day
= 1/2x + 1/2(5-x) =1/2(1/x + 1/(5-x)) = 5/2x(5-x)
since A and B complete the work in 8/5 days.
so 5/2x(5-x) = 1÷ 8/5
5/2x(5-x) = 5/8
after cross multiplication and solve we get
x^2 -5x +4 = 0
x^2 -4x -x + 4 = 0
x(x-4) -1(x-4) = 0
(x-4)(x-1) = 0
x = 4 or x = 1
since A is more efficient than B means A take less time to complete work than that of B.
So x= 1
then 5-1 = 4
here B completes 1/2 work in 4 days.
So B will complete work in 2× 4 days= 8 days
To make sure you are not studying endlessly, EduRev has designed Bank Exams study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Bank Exams.