Time and Work
Time and Work
As we all know that the amount of work done by a person varies directly with the time taken by him (her) to complete it .Thus, if a man can complete a piece of work in 10 days, then by unitary method,we can say that in one day he will do only th part of the total work. On the other hand ,if a man completes
th of the work in one day , he will take 10 days to complete the work .Thus, we obtain the following rules:
Illustration: Together, Chandu and Monu plough a field in 4 days . Monu alone takes 6 days to plough the same field .In how many days can Chandu alone plough the field ?
Solution: We have, time taken by Chandu and Monu plough the field together = 4 days.
Time taken by Monu to plough the field = 6 days. Chandu and Monu 1 day work =
Monu 1 day work = . Now, Chandu 1 day works = (Chandu and Monu 1 days work ) - (Monu 1 days work )
Hence, Chandu can plough the field in 12 days.
Illustration: A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. In how many days will they finish it together and separately?
Solution: We have, A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days
So, A and B's 1 day's work = ..............................(1)
B and C's 1 day's work = ..............................(2)
C and A's 1 day's work = ..............................(3)
Adding equations (1), (2), (3) we have
2(A + B + C)'s 1 day's work =
Hence, (A + B + C)'s 1 day's work
(A + B + C)'s 1 day's work =
Hence, A, B and C together can finish the work in 10 days.
Now,
A's 1 day's work = (A, B,and C's 1 day's work ) - (B and C's 1 day's work)
So, A alone can finish the work in 30 days.
Now,
B's 1 day's work = (A, B,and C's 1 day's work ) - (A and C's 1 day's work)
So, B alone can finish the work in 20 days.
Now,
A and B can do a piece of work in 10 days, B and C in 15 days,C and A in 20 days. How many days will be taken by A,B,and C working together to finish the work? | |||
| Right Option : B | |||
| View Explanation | |||
It takes 5 people about 18 days to construct a room. If we employ 15 people, then how may days will they take to construct the room? | |||
| Right Option : A | |||
| View Explanation | |||
Which of the quantities does not vary directly with each other? | |||
| Right Option : D | |||
| View Explanation | |||
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