Page 162 - Start Up Mathematics_8 (Non CCE)

10 Time and Work

Time is directly proportional to work. In other words, more the amount of work done by a person, more is the
time needed to do it.

Ê 1ˆ
If a person P completes a work in n days, then the work completed by him in one day is Á ˜ . Conversely, if
n¯
Ë
Ê 1ˆ
a person P completes Á ˜ work in one day, then he will take n days to complete the work.
n¯
Ë
Example 1: Honey can paint a shirt in 15 days and Kini can paint the same shirt in 20 days. If they work
together, in how many days will the shirt be painted?
Solution: Honey can paint the shirt in 15 days.
1
\ Honey’s 1 day work =
15

Kini can paint the shirt in 20 days.

1
\ Kini’s 1 day work =
20
\ Honey’s and Kini’s 1 day work = 1 + 1 = 43+ = 7
15 20 60 60
7
If Honey and Kini work together, of the work is completed in 1 day.
60
7 60 4
\ 1 work will be completed in 1 ÷ days = 1 ¥ = 8 days ª 9 days.
60 7 7
Hence, Honey and Kini can together paint the shirt in 9 days.
Example 2: Manav and Aditya can do a piece of work in 6 days. Manav alone can do the same piece of
work in 30 days. Find the number of days in which Aditya alone can complete the work.
Solution: Manav and Aditya can do a work in 6 days.

1
\ Manav and Aditya’s 1 day work =
6
Manav alone can do the work in 30 days.

1
\ Manav’s one day work =
30
Hence, Aditya’s one day work = (Aditya and Manav’s 1 day work) – (Manav’s 1 day work)
1 1 51- 4 2
= - = = =
2 6 30 30 30 15
Aditya can do work in 1 day
15 2
1
\ Aditya can do 1 work in 1 ÷ days = 1 ¥ 15 days = 7 days
15 2 2
1
Hence, Aditya can alone complete the work in 7 days.
2