People Joining and Leaving the work
There are situations in which some people are added or removed, depending on requirement, to complete the work.
In these type of questions:
1. The individual time taken to complete the work is given.
2. Person joined / leaving the work is mentioned.
3. Asked to calculate the time / total time to finish the work.
How to tackle these problems at competitive level to attempt in least time. Here is the approach.
Before this, lets understand some basics:
Let A = 5/8
Means A is capable of doing work for 8 days but, is doing only 5 days.
abd B = 3/7
Means B is capable of doing work for 7 days but, is doing only 3 days.
If we understand this concept, the things will be so easy.
Approach:
1. Work completed = 1 (Work must be completed)
2. Who is starting the work (A or B or Both)
3. Who is ending the work (A or B or Both)
If we try to find out these, our task becomes easy.
By forming a simple linear equation the problem is solved.
Example:
X and Y can do a work in 25 and 20 days respectively. Both together work for 5 days and then X leaves off. how many days will Y take to finish the rest work?
Sol: Work completed = 1
Who is starting = Both X & Y
Who is ending = Y (Since X left the work)
X + Y = 1
(5/25) + [(5+x)/20] = 1
Here x is extra days taken by Y to finish rest work (X left after 5 days).
Therefore,
1/5 + (5+x)/20 = 1
4 + 5 + x = 20 (LCM = 20)
x = 20 - 9 = 11 days
NOTE: 1. Total work is completed in = 5+11=16 days
2. Remaining work is completed in = 11 days
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Example:
A and B can do a piece of work in 20 and 12 days respectively. A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work lsat?
Sol: Work completed = 1
Who is starting = A
Who is ending = A&B
here A already worked for 4 days and joined by B.
A + B = 1
[(4+x)/20] + (x/12) = 1
3*(4+x) + 5*x = 1*60 (LCM = 60)
on solving we get, x = 6 days.
In the question, How long did the work lsat, means total days. Therefore the work is last for 4 + 6 = 10 days.
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Example:
A, B and C can complete a piece of work in 10, 12 and 15 days respectively. They started the work together, but A left the work before 5 days of its completion. B also left the work 2 days after A left. In how many days was the work completed?
Sol: Work completed = 1
Who is starting = A, B and C
Who is ending = C
C worked from starting to ending (assume he took X days)
A + B + C = 1
(X-5)/10 + (X-3)/12 + X/15 = 1
6*(X-5) + 5*(X-3) + 4*X = 1*60
6X - 30 + 5X - 15 + 4X = 60
15X - 45 = 60
15X = 60+45=105
X = 7 days
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Practice Questions
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1. A can do a piece of work in 12 days and B in 15 days. They work together for 5 days and then B left. The days taken by A to finish the remaining work is
A. 3 days
B. 5 days
C. 10 days
D. 12 days
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2. A and B together can do a piece of work in 12 days which B and C together do in 16 days. If A works for 5 days, B works for 7 days than C complete the remaining work in 13 days. In how much time B alone do the whole work?
A. 12 days
B. 24 days
C. 16 days
D. 48 days
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Practice more number of questions from any standard book to master the concept. Leave a comment in comment box. Share with others to help them.
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