COMPLEX PROBLEMS ON TIME & WORK
While we would like to solve the problems on the unitary method involving time & work, you would have noticed that the more the number of people the less the time it takes to complete a job. In such problems we assumed that all the people work at the same rate or are equally efficient. In this section, we will solve more complex time work problems, some of which will involve different efficiencies. Remember the following points in such a case.
1
A) If A completes a job in m days than A does ---------
m
of the work in 1 day
1
B) If B does the same job in n days then B dose ------- of
n
the work in 1 day
1 1 m + n
C) Together A & B do ------- + ------- or -----------
m n mn
of the work in 1 day
m + n
D) Together they can do the whole (= 1) job in 1 ÷ ----------
mn
mn
= --------- (Ans.)
m + n
Problem & Solution –
Example.1) Mr. Richard can do a job in 12 days, so find –
a) what part of the job will he do in a day
b) what part of the job will remain unfinished after 8 days
Ans.)
a) As per the given condition, Mr. Richard can complete the job in 12 days. 1
So, in 1 day he can do --------- of the job
12
b) 1
Mr. Richard in 1 day he can do --------- of the job
12
8 2
So, by 8 days he can do the job = -------- = --------
12 3
So, the part of the job that will be unfinished after 8 days
2
= 1 - ---------
3
3 - 2 1
= ---------- = ---------- (Ans.)
3 3
Example.2) Mr. Powel can assemble a computer in 2 hours, while Mr. Donald can do so in 4 hours. If they work together, how much time will they take to assemble (a) 1 computer, (b) 6 computers ? (c) if they are paid $ 1800 for their work, find each person’s share
(a) 1 computer
Ans.) Mr. Powel by 2 hours can assemble 1 computer
By 1 hour can assemble 1 / 2 computer
Mr. Donald by 4 hours can assemble 1 computer
By 1 hour can assemble 1 / 4 computer
Together by 1 hour, they can assemble
1 1 2 + 1
= -------- + --------- = -----------
2 4 4
3
= -------- of a computer
4
Suppose the whole part of the computer is 1
3
So, they together can assemble ------- part of computer
4
by 1 hour 3
1 part of the computer can be built by = 1 ÷ --------
4
4 1
= 1 X -------- = 1 --------
3 3
= 1 hour 20 minutes
(b) 6 computers
Ans.) Mr. Powel & Mr. Donald together can assemble 6 computers by
4
= 6 X -------- 3
= 2 X 4 = 8 hours. (Ans.)
(c) if they are paid $ 1800 for their work, find each person’s share
Ans.) Mr. Powel, by 1 hour can assemble 1 / 2 computer
Mr. Donald, by 1 hour can assemble 1 / 4 computer
Now, the ratio of their work is Powel : Donald
1 1
= -------- : --------
2 4
= 2 : 1
So, obtained money should be divided into 2 : 1 ratio
Now as per the given condition, $ 1800 has been shared between Mr. Powel & Mr. Donald 2
So, Mr. Powel should get the money = $ 1800 X ---------
2 + 1
2
= $ 1800 X -------- = $ 1200
3
1
So, Mr. Donald should get the money = $ 1800 X ---------
2 + 1
1
= $ 1800 X -------- = $ 600
3
So, we can conclude that, Mr. Powel will get $ 1200 and Mr. Donald should get $ 600 (Ans.)
Example.3) A can do a job in 25 days and B can do it in 30 days, they work together for 5 days and then A falls ill, in how many days will B finish the remaining part of job ?
Ans.) As per the given condition –
A can do a job in 25 days
1
So, A in 1 day can do the job = ---------
25
B can do the job in 30 days
So, B can do the job in 30 days
1
So, B in 1 day can do the job = -----------
30
So, in 1 days together they can execute the job
1 1
= -------- + ---------
25 30
6 + 5 11
= ----------- = ---------
150 150
So, in 5 days together they can execute the job -
11 11
= 5 X --------- = ----------
150 30
If we consider the whole part of the job is 1
11
Then the remaining job is = 1 - ---------
30
30 – 11 19
= ------------ = ---------
30 30
Now, after the illness of A, B has to complete the rest of the job 19/30.
1
So, B can finish --------- job in 1 days
30
1
Now, 1 part of job B can finish in = 1 ÷ -------- = 30 days
30
19 19
Now, -------- part of job, B can finish in = 30 X ---------
30 30
= 19 days
So, now we can conclude that, B can finish rest of the job in 19 days (Ans.)