The ratio of efficiency of A to that of B is 5:4. A starts the work alone and takes some days to do 33(1/3)% of the work while B takes 10more days than A to complete the remaining work. Find difference in time while they work alone to complete work?
Answers
Given:
The ratio of efficiency of A to that of B is 5:4.
To find:
The difference in time while they work alone to complete work
Solution:
Let the total work to be done by A and B is 300 units
The ratio of efficiency of A to that of B is 5:4.
It is given in the question that
A starts the work alone and takes some days to do 33(1/3)% of the work
It means that A had done 100 units of work
To find the time taken by A to complete this work is given by:
Time = Work done/ Efficiency
T = 100/5
20 days is taken by A to complete this work
Now the remaining work is completed by the A and B individually is given by:
BY A
200/5 = 40 days
By B
200/4 = 50 days
Now you can see that B takes 10more days than A to complete the remaining work.
So the Total work is 300 units only
So the time taken by A and B individually to complete the whole work is given by:
By A
Time = Work done/ Efficiency
T₁ = 300/5
T₁ = 60
By B
Time = Work done/ Efficiency
T₂ = 300/4
T₂ = 75
So the difference in their time taken to complete the work is
75 - 60
15 days
Hence, The difference in time while they work alone to complete work is 15 days
5
Step-by-step explanation
Work ratio=1:2
So time ratio= 1/5 : 2/4
=1/5:1/2
Multiplying by 10 for work and time ratios,
Now work 20:30, time 2:5
But time difference should be 10, work should be multiplied by 10/3, now total work =100
100/5-100/4 =-5
ans 5