A and B separately do work in 10 and 15 days...they worked together for some days and then A completed remaining work in 5 days.how many days will A and B workrd together?
Answers
Answer to this problem is 3 days.
There are three methods to solve this problem.
Method-1 Fraction Method
A completes the work in 10 days -> In 1 day he completes 1/10 part of job.
B completes the work in 15 days -> In 1 day he completes 1/15 part of job.
Work done by A & B both in 1 day= 1/10 + 1/15
=(10+15)/(10x15) = 25/150 = 1/6
Let both A & B workd for 'x' days.
Work done by them in x day = x/6
Remaining work = 1-x/6 ………(1)
This remaining work is done by A alone in 5 days.
Hence,
Work done by A in 5 days = Remaining work
5/10 = 1-x/6 …. From (1)
x/6 = 1–1/2
x = 6*1/2
x=3
A & B worked for 3 days.
Method-2 LCM Method
Let the total units of work be LCM(10,15)=3
A does 30/10 = 3 units per day work
B does 30/15 = 2 units per day work
Together they do (3+2)=5 units of per day work.
Let say both of them worked for x days.
Work done by them in x days = 5x
Remaining work = 30–5x
This remaining work done by A alone in 5 days
Hence,
5*(A's work per day)= 30–5x
5*3=30–5x
x=3
A & B worked for 3 days.
Method-3 Percentage Method
Let the total work be 100%
A does 100/10 = 10% work in 1 day
B does 100/15 = 6.66% work in 1 day
Both A & B do (10+6.66)=16.66% work in 1 day
Let say they worked for 'x' days
In x days the complete x*16.66% work.
Remaining work = 100%-x*16.66%
This remaining work completed by A alone in 5 days
Work done by A in 5 days = 5*10%= 50%
Hence,
Remaining work = work done by A in 5 days
100 - x*16.66%=50%
x*16.66% = 100%–50%
x*16.66% = 50%
x = 50/16.66
x=3 days
A & B worked for 3 days.
Now, which method to use in exam? Obviously percentage method is out of question as it is only useful for very basic problems & can involve lot of unnecessary calculations.
LCM & Fractions both the methods have their own merits & demerits.
While LCM method is very useful to visualise the problem it involves one extra step to calculate LCM. Also It becomes difficult to use LCM method for very complex problems.
Fraction method is suitable for those who have command on fractions related calculations. It is more direct method to approach the problem & can be easily used to solve any type of problem.
Use the method that gives best results for you.
Question= A and B separately do work in 10 and 15 days...they worked together for some days and then A completed remaining work in 5 days.how many days will A and B workrd together?
Solution:
In 1-day A can do=1/10 work.
In 1-day B can do= 1/15 work.
In the final stage A finishes the work alone in 5- days. This accounts to =5/10= 1/2 work.
So 1/2 work was done by A and B.
In 1-day A and B can do= 1/10–1/15 =5/30=1/6 work.
Therefore 1/2 work would have been done by A and B in = 1/2÷ 1/6=3-days.
So And B worked together for 3- days. =÷×=÷×=÷×=÷×=÷×=÷×=÷×=÷×=÷×==÷ Another Method: Let A and B do the work together for X- days. Then,
(X+5)/10 + X/15= 1.
On simplification we get
3X+15 + 2X= 30
= 5X= 15; or X= 3
Therefore A and B worked together for 3- days. =÷×=÷×=÷×=÷×=÷×=÷×=÷×=÷×=÷×=÷×