Today I am going to share techniques to solve Time and Work question. I have already shared a technique for this chapter here.
Question - A can do a piece of work in 10 days and B can do the same work in 15 days. How long will they take to do the work together.Answer -
Question - A can do a piece of work in 10 days. A and B together take 6 days to complete the work. How long will B take to complete the work?
This topic is based on two main concepts:
- ONE DAY WORK: Unitary Method
- TOTAL WORK
A =10 days
B = 15 days
A+B = ? days
To answer we can apply two methods.
According to the first method
If A can do a piece of work in 10 days
A’s one day work = 1/10
Similarly B’s one day work = 1/15
So this method says that
⇒ To do 1/6 work (A+B) take = 1 day
⇒ To do 1 work (A+B) take = 1/ (1/6) = 1 x6/1 = 6 days
Based on this method , the shortcut would be:
SECOND METHOD :
A = 10 days
B = 15 days
⇒ Total work = 30 units
WHY 30 units ?
⇒ Remember the LCM of 10 and 15 is 30.
⇒ A does 1 work in 10 days so in one A will do = 30/10 = 3 units
⇒ B does 1 work in 15 days so in 1 day B will do = 30/15 = 2 units
⇒ So together ( A+B) complete = 3+2 = 5 units in one day
Now which method to be applied, depends upon the kind of
questions asked and your comfort level.
Solution -
Question - A can do a work in 10 days . B can do the same work in 20 days . They both started together but after 2 days A left.The remaining work was done alone by B.How long A and B both took to complete the work?
According to the second method
Now according to the third method:
⇒
⇒ Total work = 30 units
⇒ A+B take 6 days to complete 30 units
So in 1 day A+B will complete = 30/6 = 5 units
Similarly A will complete= 30/10 =3 units
⇒ And therefore B will complete = 5-3 = 2 units
Now B completes 2 units in = 1 day
⇒ B completes 1 unit in = 1/2 day
⇒ B completes 30 units = 1/2×30=15 days
The same concept could be applied in different questions of TIME AND WORK.
Work done by A in one day = 1/10
⇒So the work done by A in 2 days = 2/10
Work done by B in one day = 1/20
Work done by B in 2 days = 2/20
⇒ Again work done by B in x days = x/20
Together they completed 1 work
