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?

**Solution:**

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?

**Solution: **

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

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

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**7th Grade Math Problems**

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