Problem 11.
5 men and 2 boys working together can do 4 time as much work per hour
as a man and a boy together. compare the work of a man with that of a
boy ?
(a) 4/3 (b) 5/3
(c) 7/3 (d)2/1
Solution: (d) 2/1
Answer:
Let the work done per day by a men be M.
and the work done by a boy be B
the according to the question:
( 5M + 2B)= 4(M +B)
=> 5M - 4M = 4B - 2B
=> M = 2B
Therefore, the work on a men is twice that of the boy or 2/1.
Problem 12. A and B can do a work in 45 and 40 days respectively. they began the work together, but A left after some time and B finished the remaining work in 23 days after how many did a A left ?
(a) 21 (b)9
(c) 15 (d)30
Answer: (b)9
Solution:
B finished the remaining work in 23 days. Therefore, A and B together finished 17 days of work of B, in say D days.
Using the formula for getting the days when two men work together to get the work done,
Days( combined) = xy/(x +y) = 40x45/(85)= 1800/85
So, A and B working together could have finished the work in 1800/85 days.
But they finished 17/40 of the work and rest they left for B to finished. Using this to get
(1800/85)x(17/40) = 45/5 = 9 days
Therefore after 9 days A left.
13. 1 man or 2 women or 3 boys can do a work in 44 days then in how many days will 1 man, 1 women and 1 boy do the work ?
(a) 24 (b)38
(c)61 (d)73
Answer:(a) 24
Solution: From here, it is clear that the efficiency of the men is twice the women and the three times the boy.
Then the work done by the men in 1 day is = 1/44
and the women is = 1/88
and the boy is = 1/132
Therefore work done in 1 day by 1 men, 1 women and 1 boy = (1/44 + 1/88 + 1/132)
And let it takes D days to complete the work, then
(1/44 + 1/88 + 1/132)x D = 1
=> D= 1/(1/44 + 1/88 + 1/132) = ( 6 + 3 + 2)/(264)
D = 264/11 = 24 days
14. A group of men decided to do a work in 10 days, but five of them become absent if the rest of the group did the work in 12 days find the original number of men?
(a) 66 (b)21
(c) 30 (d)42
Answer: (c) 30
Solution:
Let there be M men initially and they would have completed the work in 10 days.
But since 5 men are absent, there are (M - 5) men and they completed the work in 10 days.
And since work was same in both the cases, we have
(M-5)x12=Mx10
=> 12M -60 = 10M
=> 2M = 60
=> M=30
Therefor the original number of men were 30.
15. A certain number of men can do a work in 60 days. if there were 8 men more it could be finished 10 days less how many men are there?
(a) 24 (b) 40
(c) 12 (d) 9
Answer: (b) 40
Solution:
Let there are M men that finishes the work in 50 days.
And since adding 8 more men decreases the number of days to (60 -10) = 50 days.
Since work is same for both the cases , we have
Mx60 = (M+8)50
=> 10M = 400
=> M = 40
Therefore, there are 40 men on the job.
16. A builder decided to build a farmhouse in 40 days. He employed 100 men in the beginning and 100 more after 35 days and completed the construction in stipulated time.If he had not employed the additional men, how many days behind schedule would it have been finished?
(a) 60 (b) 20
(c) 30 (d) 45
Answer : (d) 45
Solution:
Work done by 100 men in 1 day = 100x1= 100 men-days
Total work done by the 100 men in 35 days = 100X35 = 3500 men days
Total work done on the last five days after adding 100 additional men = 200x5=1000men days.
Therefore in men days total work done = 4500 men-days.
If the work of 4500 men-days would have been done by 100 men only the number of days it would have taken
4500 men-days/100 men = 45 days
Therefore it would have taken 45 days to complete the work.
17. A, B and C can do a work in 8, 16,24 days respectively . They all begin together. A continues to work till it finished, C leaving off 2 days and B one day before its completion. In what time is the work finished ?
(a) 23 (b)30
(c) 12 (d)5
Answer: (d)5
Solution:
Work done by A in 1 day = 1/8
Work done by A in 1 day = 1/16
Work done by A in 1 day = 1/24
And let it took D days to finish the work, then we have
Work done by A in D days + Work done by B in (D-1) days + Work done by C in )D-2) days = 1
or
D/8 + (D - 1)/16 + (D-2)/24 = 1
=> (6D + 3D - 3 + 2D - 4)/48 = 1
=> (11D - 7) = 48
=> 11D = 55
=> D = 5 days
18. There is a sufficient food for 400 men for 31 days, after 28 days, 280 men leave the place for how many days will the rest of the food last for the rest of the men ?
(a) 20 (b)25
(c) 30 (d)10
Answer: (d)10
Solution:
Total Food available for 400 men for 31 days = 400 x 31
Total food finished in 28 days = 400 x 28
Food Remaining after 28 days = 400 x 31 - 400 x 28 = 400 x 3 = 1200
No. of men left the place = 280
No. of men remaining = 400 - 280 = 120
Therefore, number of days the food will last after 28 days = 1200/120 = 10 days.
19. A takes as much time as B and C together take to finish a job. A and B working together finish the job in 10 days. C alone can do the same job in 15 days. In how many days can B alone do the same work ?
(a) 60 (b)90
(c) 120 (d)45
Answer: (a) 60
Solution:
Since A and B could finish the job in 10 days and C could finish the job in 15 days. Then Let they all work together to finish the job, then
Number of days = 10 x 15/(10 + 15) = 150/25 = 6 days
Since A is as efficient as B and C together,
and if B and C would have worked together then they would have taken double the time taken by all of them working together.
Therefore, B and C would have finished the job in 12 days.
Since, it is given that C alone could finish the job in 15 days, then let B take D days to finish the job.
Taking help of the formula for two men working together, we have,
12 = (Dx15)/(D + 15)
=> 12 D + 180 = 15D
=> 3D = 180
=> D = 60 days.
20. A started a work and left after working for 2 days then B was called and he finished the work in 9 days. Had A left the work working for 3 days B would have finished the remaining work in 6 days. In how many days can each of them working alone , finish the whole work?
(a) 5 ,15 (b) 1,13
(c) 6,9 (d)6,14
Answer: (a) 5 ,15
Solution:
It is given from the question that if A had worked 1 day more than it would have taken B 3 days less to complete the work. It means A is three times more efficient than B.
Let it would have taken A 'D' days to complete the work alone then it would have taken B 3D days to complete the work alone.
The according to the question,
We have,
2/D + 9/3D = 1
=>6 + 9 = 3D
=> 15 = 3D
=> D = 5
and 3 D = 15 days
Therefore, it would have taken A 5 days to complete the work and B 15 days to complete the work.
(a) 4/3 (b) 5/3
(c) 7/3 (d)2/1
Solution: (d) 2/1
Answer:
Let the work done per day by a men be M.
and the work done by a boy be B
the according to the question:
( 5M + 2B)= 4(M +B)
=> 5M - 4M = 4B - 2B
=> M = 2B
Therefore, the work on a men is twice that of the boy or 2/1.
Problem 12. A and B can do a work in 45 and 40 days respectively. they began the work together, but A left after some time and B finished the remaining work in 23 days after how many did a A left ?
(a) 21 (b)9
(c) 15 (d)30
Answer: (b)9
Solution:
B finished the remaining work in 23 days. Therefore, A and B together finished 17 days of work of B, in say D days.
Using the formula for getting the days when two men work together to get the work done,
Days( combined) = xy/(x +y) = 40x45/(85)= 1800/85
So, A and B working together could have finished the work in 1800/85 days.
But they finished 17/40 of the work and rest they left for B to finished. Using this to get
(1800/85)x(17/40) = 45/5 = 9 days
Therefore after 9 days A left.
13. 1 man or 2 women or 3 boys can do a work in 44 days then in how many days will 1 man, 1 women and 1 boy do the work ?
(a) 24 (b)38
(c)61 (d)73
Answer:(a) 24
Solution: From here, it is clear that the efficiency of the men is twice the women and the three times the boy.
Then the work done by the men in 1 day is = 1/44
and the women is = 1/88
and the boy is = 1/132
Therefore work done in 1 day by 1 men, 1 women and 1 boy = (1/44 + 1/88 + 1/132)
And let it takes D days to complete the work, then
(1/44 + 1/88 + 1/132)x D = 1
=> D= 1/(1/44 + 1/88 + 1/132) = ( 6 + 3 + 2)/(264)
D = 264/11 = 24 days
14. A group of men decided to do a work in 10 days, but five of them become absent if the rest of the group did the work in 12 days find the original number of men?
(a) 66 (b)21
(c) 30 (d)42
Answer: (c) 30
Solution:
Let there be M men initially and they would have completed the work in 10 days.
But since 5 men are absent, there are (M - 5) men and they completed the work in 10 days.
And since work was same in both the cases, we have
(M-5)x12=Mx10
=> 12M -60 = 10M
=> 2M = 60
=> M=30
Therefor the original number of men were 30.
15. A certain number of men can do a work in 60 days. if there were 8 men more it could be finished 10 days less how many men are there?
(a) 24 (b) 40
(c) 12 (d) 9
Answer: (b) 40
Solution:
Let there are M men that finishes the work in 50 days.
And since adding 8 more men decreases the number of days to (60 -10) = 50 days.
Since work is same for both the cases , we have
Mx60 = (M+8)50
=> 10M = 400
=> M = 40
Therefore, there are 40 men on the job.
16. A builder decided to build a farmhouse in 40 days. He employed 100 men in the beginning and 100 more after 35 days and completed the construction in stipulated time.If he had not employed the additional men, how many days behind schedule would it have been finished?
(a) 60 (b) 20
(c) 30 (d) 45
Answer : (d) 45
Solution:
Work done by 100 men in 1 day = 100x1= 100 men-days
Total work done by the 100 men in 35 days = 100X35 = 3500 men days
Total work done on the last five days after adding 100 additional men = 200x5=1000men days.
Therefore in men days total work done = 4500 men-days.
If the work of 4500 men-days would have been done by 100 men only the number of days it would have taken
4500 men-days/100 men = 45 days
Therefore it would have taken 45 days to complete the work.
17. A, B and C can do a work in 8, 16,24 days respectively . They all begin together. A continues to work till it finished, C leaving off 2 days and B one day before its completion. In what time is the work finished ?
(a) 23 (b)30
(c) 12 (d)5
Answer: (d)5
Solution:
Work done by A in 1 day = 1/8
Work done by A in 1 day = 1/16
Work done by A in 1 day = 1/24
And let it took D days to finish the work, then we have
Work done by A in D days + Work done by B in (D-1) days + Work done by C in )D-2) days = 1
or
D/8 + (D - 1)/16 + (D-2)/24 = 1
=> (6D + 3D - 3 + 2D - 4)/48 = 1
=> (11D - 7) = 48
=> 11D = 55
=> D = 5 days
18. There is a sufficient food for 400 men for 31 days, after 28 days, 280 men leave the place for how many days will the rest of the food last for the rest of the men ?
(a) 20 (b)25
(c) 30 (d)10
Answer: (d)10
Solution:
Total Food available for 400 men for 31 days = 400 x 31
Total food finished in 28 days = 400 x 28
Food Remaining after 28 days = 400 x 31 - 400 x 28 = 400 x 3 = 1200
No. of men left the place = 280
No. of men remaining = 400 - 280 = 120
Therefore, number of days the food will last after 28 days = 1200/120 = 10 days.
19. A takes as much time as B and C together take to finish a job. A and B working together finish the job in 10 days. C alone can do the same job in 15 days. In how many days can B alone do the same work ?
(a) 60 (b)90
(c) 120 (d)45
Answer: (a) 60
Solution:
Since A and B could finish the job in 10 days and C could finish the job in 15 days. Then Let they all work together to finish the job, then
Number of days = 10 x 15/(10 + 15) = 150/25 = 6 days
Since A is as efficient as B and C together,
and if B and C would have worked together then they would have taken double the time taken by all of them working together.
Therefore, B and C would have finished the job in 12 days.
Since, it is given that C alone could finish the job in 15 days, then let B take D days to finish the job.
Taking help of the formula for two men working together, we have,
12 = (Dx15)/(D + 15)
=> 12 D + 180 = 15D
=> 3D = 180
=> D = 60 days.
20. A started a work and left after working for 2 days then B was called and he finished the work in 9 days. Had A left the work working for 3 days B would have finished the remaining work in 6 days. In how many days can each of them working alone , finish the whole work?
(a) 5 ,15 (b) 1,13
(c) 6,9 (d)6,14
Answer: (a) 5 ,15
Solution:
It is given from the question that if A had worked 1 day more than it would have taken B 3 days less to complete the work. It means A is three times more efficient than B.
Let it would have taken A 'D' days to complete the work alone then it would have taken B 3D days to complete the work alone.
The according to the question,
We have,
2/D + 9/3D = 1
=>6 + 9 = 3D
=> 15 = 3D
=> D = 5
and 3 D = 15 days
Therefore, it would have taken A 5 days to complete the work and B 15 days to complete the work.
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