IMPORTANT FACTS AND FORMULAE
1. If a person say A can do a piece of work in n days, then
A's 1 day's work = (1/n).
2. On the other hand If A’s 1 day's work = (1/n),then
A can finish the work in n days.
3. A is twice as good a workman as B, then:
The Ratio of work done by A and B = 2 : 1.
The Ratio of times taken by A and B to finish a work = 1 : 2
SOLVED EXAMPLES
Ex. 1. Worker A takes 8 hours to do a particular job. Worker B takes 10 hours to do the same Job. Then how long should it take both A and B, working together but independently, to do the same job?
Sol. A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
Ex. 2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Ex 3 .45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
1 man's 1 day's work = 1/720
45 men's 6 days' work =(1/16*6)=3/8
Remaining work =(1-3/8)=5/8
75 men's 1 day's work = 75/720=5/48
Now, 5/48 work is done by them in 1 day.
5/8 work is done by them in (48/5 x 5/8) = 6 days.
Ex. 4. A and B working separately can do a piece of work in 9 and 12 days respectively, If they work for a day alternately, A beginning, in how many days, the work will be completed?
Work done in 5 pairs of days =(5*7/36)=35/36
Remaining work =(1-35/36)=1/36
On 11th day, it is A’s turn. 1/9 work is done by him in 1 day.
1/36 work is done by him in(9*1/36)=1/4 day
Total time taken = (10 + 1/4) days = 10 1/4days.
Ex. 5. A can do a piece of work in 80 days. He works at it for 10 days B alone finishes the remaining work in 42 days. In how much time will A and B working together, finish the work?
Sol. Work done by A in 10 days =(1/80*10)=1/8
Remaining work = (1- 1/8) =7/ 8
Now,7/ 8 work is done by B in 42 days.
Whole work will be done by B in (42 x 8/7) = 48 days.
A’s 1 day's work = 1/80 and B's 1 day's work = 1/48
(A+B)'s 1 day's work = (1/80+1/48)=8/240=1/30
Hence, both will finish the work in 30 days.
Written
In Aptitude, Concepts, Time And Work
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