Time and work mathematical problem and solutions

Time and work mathematical problem and solutions

Time and work mathematical problem and solutions

Time and work mathematical problem and solutions

 

Work is defined as the amount of job assigned or the amount of job actually done.

work is always considered as a whole or 1.

1.  If A can do a piece of work in ‘a’ number of days, then in one day (1/a)th of the work is done.

Conversely, if a man does (1/a)th of a work in 1 day, then he can complete the work in 1/(1/a)= a day.

2. If A is ‘x’ times as good a workman as B, then he will take (1/x)th of the time taken by B to do the same work.

3. If A and B can do a piece of work in ‘x’ and ‘y’ days respectively, then working together, they will take {xy/(x+y)} days to finish the work and in one day, they will finish {x+y/xy}th part of the work.

4. To compare the work done by different people, first find the amount of work each can do in the same time.

N1× R1× D1= N2×R2×D2  = W

 where,
 N= number of men
D= number of days
W= total work done
R= rate of work done per man per day
5. If the number of men to do a job is changed in the ratio a:b, then the time required to do the work will be in the ratio b : a assuming the amount of work done by each of them in the given time is the same, or they are identical.
6. If two men A and B together can finish a job in ‘x’ days and if A working alone takes ‘a’ days more than A and B working together and B working alone takes ‘b’ days more than A and B working together, then x= √ab.
Example:1 Deepak can do a piece of work in 5 days and Mahesh can do the same work in 7 days. If both work together, they will finish the work in how many days?
Solution:
Deepak does work = 5 days
Mahesh do the same work= 7 days
Both will finish together= (5×7)÷(5+7)
                                         =35/12
Example:2 A man undertakes to do a certain work in 150 days. He employs 200 workers. He discovers that only a quarter of the work is done is 50 days. in order to complete the work on schedule, he must additionally employ?
Solution: 200 persons do 1/4 of the work in 50 days
1 person does 1/4 of work in 50×200 days

1 person does 3/4 of work in 3×50×200 days

n person do 3/4 of the work in 3×50×200/n days

3×50×200/n= 100

n=300
Already 200 workers are there, so 100 more workers are being employed.

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