## Time and Work Practice Problems – Set 3

Time and Work Practice Problems – Set 3
1. Sailesh worked for 2 hr and then Mahendra joined him. Sailesh then worked for four more hours and then left the work. After Sailesh left, Mahendra took another 20 hr to complete the remaining work. If both of them work together they can complete the work in 18 hr. How many hr will Sailesh and Mahendra take respectively to complete the work if they work separately?
a) 20 hr, 35 hr
b) 24 hr, 36 hr
c) 36 hr, 24 hr
d) 54 hr, 27 hr
e) 57 hr, 24 hr
Explanation:
Number of hours Sailesh worked= 2+4=6hours
Mahendra worked for (4+20)=24hours
Let Sailesh can complete the work alone in S hours and Mahendra can complete the work alone in M hours Per hour work of Sailesh = 1/S
And that of Mahendra =1/M
Therefore,
1/S+1/M=1/18
Or,18/S+18/M=1……..Equation (1)
As per question, Sailesh worked for 6 hours and Mahendra for 24 hours to complete the work
=> 6*(1/S)+ 24*(1/M)=1…….Equation (2)
Operate (1) – 3 × (2)
18/S + 18/M - 18/S - 72/M = 1 - 3
=> -54/M= -2 => M = 27
On substituting the value of R in eq.(1) we get S=54

2. 12 men and 16 women together can complete a work in 26 days while 10 women and 18 children together can complete the work in 20 days. Also 8 men and 16 children can complete the work in 25 days. 1 man, 1 woman and 1 child start the work and from 2nd day onwords every day 1 new man, 1 new woman and 1 child join the work. On which day the work shall be completed?
a) 20th day
b) 21st day
c) 22nd day
d) None of these
e) Can’t be determined
Explanation:
LCM of 26,20 and 25=1300
Let the total work be 1300 unit
Let ‘m’ be the units of work done by 1 man in 1day
‘w’ be the units of work done by 1 woman in 1 day
And ‘c’ be the units of work done by 1 child in 1 day
26(12m+16w)=1300…….(1)
20(10w+18c)=1300……..(2)
25(8m+16c)=1300……….(3)
On solving equation (1), (2) and (3);
We get, m=1.5units, w=2units and c=2.5units
Work done on day 1 = 1.5+2+2.5 = 6*1units
Work done on day 2 = (6+6*1) = 6*2units
Work done on day 3 = 6*3units
Let the work is completed on nth day
6*1+6*2+…….+6n≥1300
6n(n+1)/2 ≥ 1300
3n(n+1) ≥1300
The smallest integer value of n satisfying the above equation will be the required number of days
For n=20
3n(n+1)=1260
For n=21
3n(n+1)=1386≥1300
Therefore, the work shall be finished on 21st day.

3. A and B can do a piece of work in 20 days and 25 days respectively. They began working together but A leaves the work after X days and B complete the remaining work in 7 days. If instead of A, B had left the work after X days. Find the ratio of numbers it would A to finish the remaining work to the number of days in which B finished the remaining work?
a) 8/5
b) 4/9
c) 5/6
d) 4/5
e) 6/7
Explanation:
A does 5% work per day and B does 4% work per day.
Together they do 9% work per day.
In seven days, B does 28% work.
Hence A and B must have completed 72% work when they worked together. This implies that A left after working for 8Days.
If B had left the work after 8 days, A would have taken 28/5 days to complete the work.
Required ratio= 28/(5*7)=4/5

4. A, B and C are there people who can complete a work in 10, 20 and 25 days respectively. What is the minimum number of days required to complete the work if not more than 2 people among them work on the same day and no 2 consecutive days have the same pair of people working?
a) 7
b) 6
c) 103/15
d) 28/3
e) 82/7
Explanation:
Let us use efficiency method to solve
Let 10 units of work needs to be completed.
So,
Efficiency of A =10%
Efficiency of B = 5%
Efficiency of C = 4%
So, A+B = 15%, B+C=9% and A+C=14%.
To reduce the number of days we have to select the pair with more Efficiency. So, if we select A+B and A+C alternately
We will get our value,
So, 15+14+15+14+15+14=87% work is done in 6 days.
So, The remaining 13% can be done in 13/15 days.
So, minimum number of days required is 6+13/15=103/15days.

5. In a group. X men work an efficiency E, men work with efficiency 4E. The group complete Job- A in 13 days in which total effort required was 10001E man-days. In another group X men work with efficiency 2E and Y man work with efficiency 5E. This group completed job-B in 16 days and total effort was 1793E man-days. How long will (4X+3) men working at efficiency E and (Y+9) me working at efficiency 2E take to complete both job A and Job-B?
a) 21 days
b) 26 days
c) 15 days
d) 11 days
e) None of these
Explanation:
Man-days required to complete a job= m*d*e, where m= number of men, d=days and e= efficiency.
Hence for Job A, man-days required= x*13*E+y*13*4E=1001E
Thus 13x*E+52y*E=1001E
For Job B, man-days required= x*2E*16+y*5E*16=1792E. Thus 32x+80y=1792.
Solving for x and y, we have x=21 and y=14.
Now 4x+3=4*21+3=87 and y+9=14+9=23.Total man-days required to complete jobs A and B together=1001E+1792E=2793E man-days.
2793E=87*d*E+23*d*2E
Thus d= 2793/133=21days.

6. 25 men and 15 women can complete a piece of work in 12 days. All of them start working together and after working for 8 days the women stopped working. 25 men complete the remaining work in 6 days. how many days will it take for completing the entire job if only 15 women are put on the job ?
a) 60 days
b) 88 days
c) 94 days
d) None of these
e) Can’t be determined
Explanation:
25 men and 15 women can complete, a piece of work in 12 days.
Work done by them in 8 days = 8/12 = 2/3
Remaining work is completed by 25 men in 6 days
Time taken by 25 men to complete the whole work = 3 x 6 = 18 days
From the question
Time taken by 15 women to complete the whole work = 1 / (1/12 - 1/18)
= 1 / {(3 - 2) / 36} = 36/(3 - 2) = 36 days

7. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
a) 1 ½ min
b) 3 ½ min
c) 3 3/5 min
d) 4 ¼ min
e) 2 ¾ min
Explanation:
1 minute's Work of both the punctures = (1/9+1/6)=5/18
So, both the punctures will make the tyre flat in 18/5 = 3 3/5 min

8. P, Q and R are three typists who working simultaneously can type 216 pages in 4 hours. In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour ?
a) 14, 17, 20
b) 15, 17, 22
c) 15, 18, 21
d) 16, 18, 22
e) 14, 18, 21
Explanation:
Let the number of pages typed in one hour by P, Q and R be x, y and z respectively. Then,
x + y + z = 216/4 => x + y + z = 54 … (i)
z – y = y – x => 2y = x + z …. (ii)
5z = 7x => x = 5z/7 …. (iii)
Solving (i), (ii) and (Hi), we get x = 15, y = 18, z = 21.

9. If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?
a) 10 days
b) 12 days
c) 6 days
d) 8 days
e) None of these
Explanation:
Let A and B together complete the work in x days.
Then, time taken by A = (x + 4) days
And, time taken by B = (x + 16) days
Now, according to the question,
[1/(x + 4)] + [1/(x + 16)] = 1/x
=> (x + 16 + x + 4)/[(x + 4)(x + 16) = 1/x
=> 2x^2 + 20x = x^2 + 20x + 64
=> x^2 = 64 => x = 8 days

10. A machine A can print one thousand books in 10 hours, machine B can print the same number of books in 12 hours while machine C print them in 15 hours. All the machines are started at 9 a.m. while machine A is closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?
a) 11:30 a.m.
b) 12 noon
c)  12:30 pm
d) 2:20 pm
e) None of these