**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.

N_{1}× R_{1}× D_{1}= N_{2}×R_{2}×D_{2 = 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

n=300

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