# Time and Work

1. If A can do a piece of work in n days, then A’s 1 day work = 1/n

2. If A’s 1 day’s work = 1/n, then A can finish the work in n days.

Example: If A can do a piece of work in 4 days,then A’s 1 day’s work = 1/4. If A’s 1 day’s work = 1/5,

then A can finish the work in 5 days

3. If A is thrice as good workman as B,then: Ratio of work done by A and B = 3:1. Ratio of time taken

by

A and B to finish a work = 1:3

4. Definition of Variation: The change in two different variables follow some definite rule. It said that the

two variables vary directly or inversely. Its notation is X/Y = k, where k is called constant. This variation

is called direct variation. XY = k. This variation is called inverse variation.

**5. Some Pairs of Variables: **

**i. Number of workers and their wages. If the number of workers increases, their total wages increase. **

**If the **

**number of days reduced, there will be less work. If the number of days is increased, there will be **

**more work. **

**Therefore, here we have direct proportion or direct variation. **

**ii. Number workers and days required to do a certain work is an example of inverse variation. If more **

**men are **

**employed, they will require fewer days and if there are less number of workers, more days are **

**required. **

**iii. There is an inverse proportion between the daily hours of a work and the days required. If the **

**number of **

**hours is increased, less number of days are required and if the number of hours is reduced, more **

**days are **

**required. **

**6. Some Important Tips: **

*More Men – Less Days and Conversely More Day – Less Men. *

*More Men – More Work and Conversely More Work – More Men. *

*More Days – More Work and Conversely More Work – More Days. *

*Number of days required to complete the given work = Total work/One day’s work. *

**Since the total work is assumed to be one(unit), the number of days required to complete the given work would be the reciprocal of one day’s work. Sometimes, the problems on time and work can be solved using the proportional rule ((man*days*hours)/work) in another situation. **

**7. If men is fixed,work is proportional to time. If work is fixed, then time is inversely **

**proportional to men therefore, **

**(M1*T1/W1) = (M2*T2/W2) **

**Problems on Time and Work **

**1) If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day **

**can do it in how many days? **

**Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2) **

**so (9*6*88/1) = (6*8*d/1) **

**on solving, d = 99 days. **

**2) If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man **

**should **

**be engaged to finish the rest of the work in **

**6 days working 9 hours a day? **

**Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2) **

**so, (34*8*9/(2/5)) = (x*6*9/(3/5)) **

**so x = 136 men **

**number of men to be added to finish the work = 136-34 = 102 men **

**3) If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls **

**can do **

**the same work? **

**Solution: Given that 5 women is equal to 8 girls to complete a work **

**so, 10 women = 16 girls. **

**Therefore 10women +5girls = 16girls+5girls = 21 girls. **

**8 girls can do a work in 84 days **

**then 21 girls ————— ? **

**Answer = (8*84/21) = 32 days. Therefore 10 women and 5 girls can a work in 32 days **

**4) Worker A takes 8 hours to do a job. Worker B takes 10hours to do the same job. How long it **

**take **

**both A & B, working together but independently, to do the same job? **

**Solution: A’s one hour work = 1/8. **

**B’s one hour work = 1/10 **

**(A+B)’s one hour work = 1/8+1/10 = 9/40 **

**Both A & B can finish the work in 40/9 days **

**5) A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, **

**working together, what part of the same work they can finish in a day? **

**Solution: Given that B alone can complete the same work in days = half the time **

**taken by A = 9days **

**A’s one day work = 1/18 **

**B’s one day work = 1/9 **

**(A+B)’s one day work = 1/18+1/9 = 1/6 **

**6) A is twice as good a workman as B and together they finish a piece of work in 18 days.In how **

**many **

**days will A alone finish the work. **

**Solution: if A takes x days to do a work then **

**B takes 2x days to do the same work **

**= > 1/x+1/2x = 1/18 **

**= > 3/2x = 1/18 **