Learn how to solve problems on time and work in different situations when time required to complete a piece of work and when the work done in a given period of time.
Case I: If a person A completes a piece of work in n days, then work done by A in one days = 1/n th part of the work.
Case II: If a person A completes 1/n th part of work in one day, then A will take n days to complete the work.
Now we will learn how to use the concept of time and work for solving various problems.
Word problems on time and work:
1. Adam is thrice as good a workman as Brain and together they finish the piece of work in 15 days. In how many days will Adam alone finish the work?
Adam’s 1 day’s work: Brain’s 1 day’s work = 3 : 1
(Adam + Brain)’s 1 day’s work = 1/15
Now, divided 1/15 in the ratio 3 : 1
Therefore, Adam’s 1 day’s work = 1/15 × 3/4 = 1/20
Therefore, Adam alone can finish the work in 20 days.
2. Archie, Benjamin, Christopher can finish a piece of work in 10 days, 12 days and 15 days respectively. If all the three work at it together, they are paid $ 600 for the whole work. How should the money be divided among them?
Archie’s 1 day’s work = 1/10
Benjamin’s 1 day’s work = 1/12
Christopher’s 1 day’s work = 1/15
Therefore, ratio of shares of Archie, Benjamin, Christopher = Ratio of their 1 day’s work.
= 1/10 : 1/12 : 1/15
= 6 : 5 : 4
Sum of ratio terms = 6 + 5 + 4 = 15
Therefore, Archie’s share = $ 6/15 × 600 = 6 × 40 = $ 240
Benjamin’s share = $ 5/15 × 600 = 5 × 40 = $ 200
Christopher’s share = $ 4/15 × 600 = 4 × 40 = $ 160
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