TYPES OF RATIOS:
11. TIME AND WORK
1. Usually, we need to complete a particular job in a reasonable time.
2. We need to complete any project earlier or later depending upon the requirements.
3. Accordingly, the men on duty have to be increased or decreased.
4. This means, the time allowed and the men engaged for a project are inversely proportional to each other. Again it means, more the number of men involved, the lesser is the time required to finish a job.
5. You also come across the situations where time and work or men and work are in direct proportion to each other.
Formulae:
1. If A can do a piece of work in n days, then at a uniform rate of working, A will finish nth
1 work in one day.
2. If th n
1 of work is done by A in one day, then A will take n days to complete the full work.
3. If A does th n
1 of a work in m hours, then A will take m
n hours.
4. If A does three times faster work than B, then a) The ratio of work done by A and B is 3 : 1 b) The ratio of time taken by A and B is 1 : 3
5. A, B and C can do a piece of work in T1, T2 and T3 days respectively. If they have worked for D1, D2 and D3 days respectively, then
a) Amount of work done by A =
1 1
T D
b) Amount of work done by B =
2 2
T D
c) Amount of work done by C =
3 3
T D
d) Amount of work done by A, B and C together = . T +D T +D T D
3 3 2 2 1 1
6. If A can do a piece of work in X days and B can do the same work in Y days, then both of them working together will do the same work in
Y + X
XY days.
7. If A, B and C, while working alone, can complete a work in X, Y and Z days respectively, then they will together complete the work in
ZX + Y Z + XY
XY Z days.
8. A and B working together can complete a piece of work in X days. If A working alone can complete the work in Y days, then B working alone will complete the work in
X
10. If A and B working together can complete a work in X days and B is k times efficient than A, then
c) The time taken by both A and B working together to complete the work is . k 11. If A working alone takes a days more than A and B working together. If B worked
alone, he takes b hours more to complete the job than A and B working together then both A and B working together can finish the job in
ab
days.12. If A can complete taken by both A and B working together to complete the work is .
k 1
x
15. If A is k times more efficient than B and hence able to finish the work in l days less than B, then
c) A and B working together, can finish the work in 1 k
kl
2 days.
16. There are two groups of people with same efficiency. In one M1 persons can do W1 works in D1 time and in the other M2 persons can do W2 works in D2 time. Then the relationship between the two groups is M1D1W2 M2D2W1
17. There are two groups of people with same efficiency. In one M1 persons can do W1
works in D1 time working t1 hours a day and in the other M2 persons can do W2 works in D2 time working t2 hours a day. Then the relationship between the two groups is
1
SOLVED EXAMPLES
1. A can complete a piece of work by working alone in 5 days and B while working alone can finish the same work in 10 days. If both of them work together, then in how many days, the work will be finished.
Sol: Here, X = 5, Y = 10
Working together, A and B will finish the work in Y many days would all of them complete the same work working together?
Sol: Here, X = 5, Y = 10, Z = 13 this work in 15 days, how long would B take to complete the same work?
Sol: Here, X = 10, Y = 15 Madhu in 20 days. How long would each take separately to do the same work?
Sol: Here, X = 12, Y = 15 and Z = 20
Sunil alone can do the work in
ZX
5. Mukesh can do a piece of work in 16 days. If Nita works thrice as fast as Mukesh, how long would they take to finish the work by working together?
Sol: Here, X = 16 and k = 3 in a given time, how long A alone would take to do the work?
Sol: Here, X = 4 and k = 2
Time taken by A, working alone = 4 6
7. A alone would take 7 days more to complete the work than if both A and B worked together. If B worked alone, he took
4
1 days more to complete the job both worked 3 together. What time would they take if both A and B worked together?
Sol: Here, a = 7, b = than B takes. Find the time in which B alone can complete the work.
Sol: Here, k = 4 and l = 12
10. If 12 persons can complete th 5
1 of a work in 4 days, then find the number of persons required to complete the remaining work in 16 days.
Sol: Here M1 = 12, D1 = 4, W1 =
11. If 5 persons can cut 15 trees in 6 days working 10 hours a day. Then, in how many days can 12 persons cut 36 trees working 6 hours a day.
Sol: Here M1 = 5, D1 = 6, W1 = 15, t1 = 10 women would complete the work?
Sol: Here, a = 8, b = 12, c = 5, d = 3 and n = 21 they do it together?
1. 24 2. 9 3. 10 4. 7
2. Madan and Raju can do a work in 15 days, if they work together. If Madan alone can do it in 20 days, in how many days Raju alone can do the work?
1. 87
4 2. 60 3. 10 4. 44
3. P and Q can do a work in 9 days. Q and R can do it in 12 days, R and P in 18 days. In how many days all of them can do the work?
1. 8 2. 9 3. 15 4. 5
4. Shweta can do a work in 40 days. She worked for 5 days and Srikanth finished the remaining work in 21 days. In how many days can both of them do the work?
1. 18 2. 19 3. 16 4. 24
5. Rajeev can do a work in 50 days, which Sanjay can do in 40 days. Rajeev started the work and was joined by Sanjay after 20 days. In how many days the total work is completed?
1. 10 2. 15 3. 33
3
1 4. 14
6. Pavan and Venu undertook a piece of work for Rs.600. Pavan alone can do the work in 24 days and Venu alone can do it in 12 days. What is the share of Venu?
1. Rs.360 2. Rs.400 3. Rs.200 4. Rs.240
7. P and Q can do a piece of work in 12 days. P, Q and R together can finish it in 8 days. In how many days will R finish that work?
1. 5
2 4 2. 24 3. 20 4. 4
8. P can do a piece of work in 80 days. He works at it for 10 days and then Q alone finishes the work in 42 days. Both together could complete the work in how many days?
1. 30 2. 48 3. 24 4. 25
9. P and Q together finish a work in 30 days. They worked for 20 days and then Q left. The remaining work was done by P alone in 15 days. In how many days P alone can finish the total work?
1. 35 2. 30 3. 45 4. None
10. P can complete a job in 9 days, Q in 10 days and R in 15 days. Q and R started the work and were forced to leave after 3 days. Find the time taken by P to complete the remaining work.
1. 4½ 2. 5 3. 7½ 4. None
11. P does half as much work as Q in three fourth of the time. If together they take 18 days to complete a work, how much time shall P take to do it?
1. 35 2. 30 3. 45 4. None
12. P can complete a job in 15 days, Q in 10 days and R in 20 days. Q and R started the work together and were forced to leave after 4 days. Find the time taken by P to complete the remaining work?
1. 5 2. 12 3. 6 4. None
13. A certain number of men complete a piece of work in 50 days. If there were 8 men more the work could be finished in 10 days less. How many men were there originally?
1. 30 2. 32 3. 36 4. 40
14. If 20 men can build a wall of 120 meters long in 6 days, what length of a similar wall can be built by 25 men in 3 days?
1. 95 2. 60 3. 75 4. 70
15. P and Q can do a piece of work in 12 days, Q and R in 15 days, R and P in 20 days. How long the work runs if they do it altogether.
1. 10 days 2. 15 days 3. 12 days 4. 5 days
16. If 17 labourers can dig a ditch 26 meters long in 18 days, working 8 hours a day, how many more labourers should be engaged to dig a similar ditch of 52 meters length in 16 days, each labourer working 9 hours a day?
1. 34 2. 17 3. 30 4. None
17. P and Q can do a piece of work in 30 and 70 days respectively. They worked together for 10 days and then Q goes away. In how many days will P finish the remaining work?
1. 11 2. 15 3. 16 4. 15
7 5
18. If 5 men or 6 women can do a piece work in 38 days, in how many days will 3 men and 4 women will do the same work?
1. 20 2. 17 3. 30 4. None
19. 2 men and 3 boys can do a piece of work in 8 days, 3 men and 2 boys can do it in 7 days. In how many days can 1 man and 2 boys do the same work?
1. 24 2. 17 3. 12 4. 14
20. P does two-fifth of work in 8 days. He then calls Q and they together complete the remaining work in 6 days. How long would Q alone take to complete the entire work?
1. 20 2. 17 3. 18 4. None
21. A job can be completed by 10 men in 20 days and by 40 women in 15 days. How many days it takes for 5 men and 5 women to finish the work?
1. 40 2. 24 3. 30 4. 35
22. After completing half of a work in 10 days P was joined by Q and they worked together for 3 days. P completed the remaining work in 4 days. In how many days Q alone can do the entire work?
1. 25 2. 20 3. 30 4. 18
23. 10 men can do a work in 40 days. They started together but 4 men left after a few days. As a result the work was completed in 60 days. After how many days the 4 men left?
1. 15 2. 20 3. 10 4. None
24. 80 men can finish 5
2 of work in 30 days. How many men are required to finish the remaining work in 60 days?
1. 38 2. 60 3. 30 4. 40
25. The work done by 1 man and 3 boys are equal. A work can be done by 3 men and 5 boys in 8 days. How many boys should assist 9 men to finish the work in 4 days?
1. 4 2. 7 3. 1 4. None
26. P and Q can do a job in 40 days and 36 days respectively. If they did a job for Rs.2660, what should be the share of Q? (in Rs.)
1. 1260 2. 1400 3. 1520 4. 1600
27. 8 men and 20 boys can construct a house in 5 days working for 6 hours a day. 5 men and 8 boys can construct two such houses in 16 days working for 7.5 hours a day. In how many days can 12 men and 6 boys construct 5 such houses working for 10 hours a day?
1. 12 2. 18 3. 24 4. 30
28. P can do a piece of work in 30 days and Q alone can do it in 40 days. They begin together but 5 days before the completion of work, P leaves off. What is the total number of days to complete the work?
1. 20 2. 30 3. 25 4. 15
29. P and Q can do a piece of work in 12 days and 20 days respectively. They started together and then P left after for some days. If Q finishes the remaining work in 12 days, how many days has P worked on it before leaving?
1. 3 days 2. 4 days 3. 6 days 4. 8 days
30. P is twice as good a workman as Q. Working together they can finish a work in 16 days. How many days will P take to finish the work?
1. 4 days 2. 8 days 3. 24 days 4. 48 days
31. P and Q can do a work in 10 and 15 days respectively. If they work at it on an alternate day, P starting first, in how many days the work will be completed?
1. 6 days 2. 10 days 3. 12 days 4. 15 days
32. A contractor agreed to complete a work in 120 days. He engaged 150 men for the work and after 70 days, only half of the work was completed. How many additional men must employ to complete the work in agreed time?
1. 60 men 2. 90 men 3. 150 men 4. 210 men
33. A camp has provision of food for 600 persons for 41 days. After 37 days, 360 persons left the camp. How long the food will last for the remaining persons?
1. 5 days 2. 8 days 3. 10 days 4. 12 days
34. P can do a job in 10 days, Q can do it in 12 days and R can do it in 15 days. All begin together, but P leaves the work after 2 days and Q leaves 3 days before the work is completed. How long did the work last?
1. 9 days 2. 8 days 3. 7 days 4. 6 days
35. P and Q can do a piece of work in 45 days and 40 days respectively. They began to work together but P leaves after „x‟ days and Q finishes the remaining work in (x + 14) days. After how many days did P leaves?
1. 19 days 2. 11 days 3. 9 days 4. 12 days
36. Shekhar has done 3
1 rd of a job in 8 days, Kamalakar completes the rest of the job in 8 days. In how many days would Shekhar and Kamalakar together had completed the work?
1. 24 days 2. 16 days 3. 20 days 4. 8 days
37. A garrison has provisions for certain number of days. After 15 days, 4
1 of the men left and if it is found that the provisions will now last just as before, how long was that?
1. 50 days 2. 60 days 3. 70 days 4. 30 days 38. If 4 labourer reap 40 acres in 30 days, how many acres will 18 labourer reap in 12 days?
1. 49 acres 2. 70 acres 3. 72 acres 4. 65 acres
39. 6 men can prepare 6 toys in 5 days working 4 hrs a day. In how many days can 10 men can prepare 15 toys working 5 hrs per day?
1. 4 2. 5 3. 6 4. 7
40. 2 men and 3 boys can do a piece of work in 10 days and 3 men together with 2 boys can do the same job in 8 days. In how many days can 2 men and a boy do the work?
1. 12 2
1 days 2. 18
2
1 days 3. 25 days 4. 25
2 1days
1) 2 11) 4 21) 3 31) 3
2) 2 12) 3 22) 2 32) 1
3) 1 13) 2 23) 3 33) 3
4) 4 14) 3 24) 2 34) 3
5) 3 15) 1 25) 3 35) 3
6) 2 16) 2 26) 1 36) 4
7) 2 17) 4 27) 2 37) 2
8) 1 18) 3 28) 1 38) 3
9) 3 19) 4 29) 1 39) 3
10) 1 20) 1 30) 3 40) 1