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TIME AND WORK
Points for recapitulation while solving problems on time and work: 1.
If a person can do a piece of work in ‘m’ days, he can do
m
1
of the work in 1 day. 2.
If the number of persons engaged to do a piece of work be increased (or decreased) in a certain ratio the time required to do the same work will be decreased (or increased) in the same ratio. 3.
If A is twice as good a workman as B, then A will take half the time taken by B to do a certain piece of work. 4.
Time and work are always in direct proportion. 5.
If two taps or pipes P and Q take ‘m’ and ‘n’ hours respectively to fill a cistern or
tank, then the two pipes together fill




n
1m
1
part of the tank in 1 hour and the entire tank is filled in
nm
mnn
1m
1
1


hours.
Examples:
1. If 12 man can do a piece of work in 36 days. In how many days 18 men can do the same work? Solution:
12 men can do a work in 36 days. 18 men can do the work in
3618
12

= 24 days. Note:
If the number of men is increased, the number of days to finish the work will decrease. 2.
A and B can finish a work in 12 days. B and C can finish the same work in 18 days. C and A can finish in 24 days. How many days will take for A, B and C combined together to finish the same amount of work? Solution:
A and B can finish the work in 12 days. (A+B) Can finish in 1 day
12
1
of the work. Similarly (B+C) can finish in
18
1
of the work. (C+A) can finish in
24
1
of the work. 2(A+B+C) can finish in 1 day (
)24
118
112
1

of the work. =
72
1372
346


of the work. (A+B+C) can finish in 1 day =
144
13
of the work. Takes you to places where you belong.
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
(A+B+C) can together finish the work in
13
144
=
13
111
days. 3.
A, B and C earn Rs.120 per day while A and C earn Rs.80 per day and B and
C earn Rs.66 per day. Find C’s earning only.
Solution:
(A+B+C) earn per day Rs.120

(1) (A+C) earn per day Rs.80

(2) (B+C) earn per day Rs.66

(3) From (1) and (2), we find that C earns Rs.40 From (3) we get, That B earns 26 since C earns Rs.40 4.
4 men or 8 women can do a piece of work in 24 days. In how many days, will 12 men and 8 women do the same work? Solution:
4 men = 8 women can do a work in 24 days. 1 man or 2 women in one day can finish
24
1
of the work. Now 12 men and 8 women together will do the work as 16 men alone can do the work. 16 men can do in one day =
3
224
16

of the work. 16 men can do the entire work in
2
3
or
2
11
days. 5. A and B can finish a work in 16 days, while A alone can do the same work in 24 days. In how many days, B alone can finish the same work? Solution:
A and B can finish a work in 16 days. (A+B) can finish in one day
16
1
of the work. A alone can finish in one day
24
1
of the work. The amount of work that B alone can do in one day
48
148
2324
116
1


of the work. B alone can complete the work in 48 days. 6. A and B can do a piece of work in 12 days. B and C can do it in 20 days. If A is twice as good a workman as C, then in what time will B alone do it? Solution:
(A+B) can do a work in 12 days. (A+B) in one day can do
12
1
of the work

(1) Similarly (B+C) in one day can do
20
1
of the work

(2) Since A=2C, in (1) put A=2C

(2C+B) in one day can do
12
1
of the work. Takes you to places where you belong.
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i.e., [(B+C)+C] in one day can do
12
1
of the work. C alone can do in one day
20
112
1

=
30
160
260
35


of work

(3) From (2), using (3), B alone can do in one day
60
160
2330
120
1


of work.

B alone can do the entire work in 60 days. 7. A contractor undertook to do a piece of work in 125 days and employs 175 men to carry out the job, but after 40 days, he finds that one a quarter of the work had been carried out. How many more men should be employed to finish the work in time? Solution:
Men Days Work 175 40
4
1
?(x) 85
4
3
x= 175

85
40

4
1
4
3
= 247 (247
–
175) or 72 men will have to be employed. 8. B is twice as fast as A and C is twice as fast as B. If A alone can complete the job in 28 days, how many days will A, B and C take to complete the job working together? Solution:
Given B = 2A C= 2B (efficiency-wise) A can complete the work in 28 days (given)

B alone can complete the work in 14 days [

B is twice as fast as A] Hence, C alone can complete the work in 7 days [

C is twice as fast as B] (A+B+C) working together can complete



7
114
128
1
part of the work in 1 day. =
4
128
728
421


of the work in one day.

(A+B+C) working together can complete the entire work in 4 days. 9. A cistern is normally filled in 6 hours, but takes 2 hours more to fill it because of a leak at its bottom. If the cistern is full, how long will it take for the leak to empty the cistern? Solution:
Takes you to places where you belong.
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The cistern is filled in 6 hours.

In 1 hour
6
1
of the cistern will be filled. Due to a leak in the cistern, in 1 hour
8
1
of the cistern only is filled.

Leakage in 1 hour =
24
124
348
16
1


of the cistern.
24
1
of the cistern is leaked out in 1 hour. The entire cistern will become empty in 24 hours. 10. Two pipes A and B are attached to a cistern. Pipe A can fill the cistern in 6 hours while pipe B can empty it in 8 hours. When both the pipes are opened together, find the time for filling the cistern. Solution:
Pipe A fills in an hour =
6
1
of the cistern. Pipe B empties in one hour
8
1
of the cistern. In 1 hour, the portion of the cistern filled =
24
18
16
1


Time taken to fill the cistern = 24 hours. 11. The efficiency of the first machine tool is 20% less than that of the 2
nd
one. The first machine tool operated for 5 hours, whereas, the second one operated for 4 hours and together they machined 4000 work pieces. Find the number of work-pieces machined by the first machine tool. Solution:
Efficiency of the two machine tools = 80: 100 = 4: 5 Time ratio of the two machine tools = 5: 4

Work ratio of the two machine tools = 4

5: 5

4 = 20: 20 = 1: 1 Thus both the machine tools produced the same number of work-pieces Viz.,
20002
4000

Alternative: The second machine operating for 4 hours = first machine operating for 5 hours. Hence the first machine would produce 4000 pieces in 10 hours. In 5 hours it would have produced 2000 pieces. 12. Two coal loading trucks handle 9000 tonnes of coal at an efficiency of 90% working 12 hours per day for 8 days. How many hours a day, 3 coal loading trucks should work at an efficiency of 80% so as to load 12000 tonnes of coal in 6 days. Solution:
Takes you to places where you belong.
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No of lorries
Efficiency
Hours of
work per day
No of days.
Tonnes
2
90%
12
8
9000
3
80%
? =X
6
12000
X=
129000
120006
880
903
2

= 16 hours.
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TIME AND WORK
Points for recapitulation while solving problems on time and work: 1.
If a person can do a piece of work in ‘m’ days, he can do
m
1
of the work in 1 day. 2.
If the number of persons engaged to do a piece of work be increased (or decreased) in a certain ratio the time required to do the same work will be decreased (or increased) in the same ratio. 3.
If A is twice as good a workman as B, then A will take half the time taken by B to do a certain piece of work. 4.
Time and work are always in direct proportion. 5.
If two taps or pipes P and Q take ‘m’ and ‘n’ hours respectively to fill a cistern or
tank, then the two pipes together fill




n
1m
1
part of the tank in 1 hour and the entire tank is filled in
nm
mnn
1m
1
1


hours.
Examples:
1. If 12 man can do a piece of work in 36 days. In how many days 18 men can do the same work? Solution:
12 men can do a work in 36 days. 18 men can do the work in
3618
12

= 24 days. Note:
If the number of men is increased, the number of days to finish the work will decrease. 2.
A and B can finish a work in 12 days. B and C can finish the same work in 18 days. C and A can finish in 24 days. How many days will take for A, B and C combined together to finish the same amount of work? Solution:
A and B can finish the work in 12 days. (A+B) Can finish in 1 day
12
1
of the work. Similarly (B+C) can finish in
18
1
of the work. (C+A) can finish in
24
1
of the work. 2(A+B+C) can finish in 1 day (
)24
118
112
1

of the work. =
72
1372
346


of the work. (A+B+C) can finish in 1 day =
144
13
of the work. Takes you to places where you belong.
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
(A+B+C) can together finish the work in
13
144
=
13
111
days. 3.
A, B and C earn Rs.120 per day while A and C earn Rs.80 per day and B and
C earn Rs.66 per day. Find C’s earning only.
Solution:
(A+B+C) earn per day Rs.120

(1) (A+C) earn per day Rs.80

(2) (B+C) earn per day Rs.66

(3) From (1) and (2), we find that C earns Rs.40 From (3) we get, That B earns 26 since C earns Rs.40 4.
4 men or 8 women can do a piece of work in 24 days. In how many days, will 12 men and 8 women do the same work? Solution:
4 men = 8 women can do a work in 24 days. 1 man or 2 women in one day can finish
24
1
of the work. Now 12 men and 8 women together will do the work as 16 men alone can do the work. 16 men can do in one day =
3
224
16

of the work. 16 men can do the entire work in
2
3
or
2
11
days. 5. A and B can finish a work in 16 days, while A alone can do the same work in 24 days. In how many days, B alone can finish the same work? Solution:
A and B can finish a work in 16 days. (A+B) can finish in one day
16
1
of the work. A alone can finish in one day
24
1
of the work. The amount of work that B alone can do in one day
48
148
2324
116
1


of the work. B alone can complete the work in 48 days. 6. A and B can do a piece of work in 12 days. B and C can do it in 20 days. If A is twice as good a workman as C, then in what time will B alone do it? Solution:
(A+B) can do a work in 12 days. (A+B) in one day can do
12
1
of the work

(1) Similarly (B+C) in one day can do
20
1
of the work

(2) Since A=2C, in (1) put A=2C

(2C+B) in one day can do
12
1
of the work. Takes you to places where you belong.
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i.e., [(B+C)+C] in one day can do
12
1
of the work. C alone can do in one day
20
112
1

=
30
160
260
35


of work

(3) From (2), using (3), B alone can do in one day
60
160
2330
120
1


of work.

B alone can do the entire work in 60 days. 7. A contractor undertook to do a piece of work in 125 days and employs 175 men to carry out the job, but after 40 days, he finds that one a quarter of the work had been carried out. How many more men should be employed to finish the work in time? Solution:
Men Days Work 175 40
4
1
?(x) 85
4
3
x= 175

85
40

4
1
4
3
= 247 (247
–
175) or 72 men will have to be employed. 8. B is twice as fast as A and C is twice as fast as B. If A alone can complete the job in 28 days, how many days will A, B and C take to complete the job working together? Solution:
Given B = 2A C= 2B (efficiency-wise) A can complete the work in 28 days (given)

B alone can complete the work in 14 days [

B is twice as fast as A] Hence, C alone can complete the work in 7 days [

C is twice as fast as B] (A+B+C) working together can complete



7
114
128
1
part of the work in 1 day. =
4
128
728
421


of the work in one day.

(A+B+C) working together can complete the entire work in 4 days. 9. A cistern is normally filled in 6 hours, but takes 2 hours more to fill it because of a leak at its bottom. If the cistern is full, how long will it take for the leak to empty the cistern? Solution:
Takes you to places where you belong.
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The cistern is filled in 6 hours.

In 1 hour
6
1
of the cistern will be filled. Due to a leak in the cistern, in 1 hour
8
1
of the cistern only is filled.

Leakage in 1 hour =
24
124
348
16
1


of the cistern.
24
1
of the cistern is leaked out in 1 hour. The entire cistern will become empty in 24 hours. 10. Two pipes A and B are attached to a cistern. Pipe A can fill the cistern in 6 hours while pipe B can empty it in 8 hours. When both the pipes are opened together, find the time for filling the cistern. Solution:
Pipe A fills in an hour =
6
1
of the cistern. Pipe B empties in one hour
8
1
of the cistern. In 1 hour, the portion of the cistern filled =
24
18
16
1


Time taken to fill the cistern = 24 hours. 11. The efficiency of the first machine tool is 20% less than that of the 2
nd
one. The first machine tool operated for 5 hours, whereas, the second one operated for 4 hours and together they machined 4000 work pieces. Find the number of work-pieces machined by the first machine tool. Solution:
Efficiency of the two machine tools = 80: 100 = 4: 5 Time ratio of the two machine tools = 5: 4

Work ratio of the two machine tools = 4

5: 5

4 = 20: 20 = 1: 1 Thus both the machine tools produced the same number of work-pieces Viz.,
20002
4000

Alternative: The second machine operating for 4 hours = first machine operating for 5 hours. Hence the first machine would produce 4000 pieces in 10 hours. In 5 hours it would have produced 2000 pieces. 12. Two coal loading trucks handle 9000 tonnes of coal at an efficiency of 90% working 12 hours per day for 8 days. How many hours a day, 3 coal loading trucks should work at an efficiency of 80% so as to load 12000 tonnes of coal in 6 days. Solution:
Takes you to places where you belong.
© ENTRANCEGURU.COM Private Limited fab58bf5-62fc-4671-a172-31cd0b11e026.doc - 5 -
No of lorries
Efficiency
Hours of
work per day
No of days.
Tonnes
2
90%
12
8
9000
3
80%
? =X
6
12000
X=
129000
120006
880
903
2

= 16 hours.
