Aptitude Time And WorkPage 3
17. | | L, M and N are three machines, which produce electronic gadgets, the efficiency of production of which are in the ratio 2:4:5. If L works for 7 days, M for 4 days and N for 2 days, they produce 1680 gadgets. How many gadgets are produced if L, M and N work for 3, 6, 4 days respectively? | | (a)1720 | | (b)1860 | | (c)2100 | | (d)2240 |
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Answer is: CLet L produce 2x books in 1 day.
so, M and N produce 4x and 5x books in 1 day.
No. of books produced by
L in 7 days = 14x
M in 4 days = 16x
N in 2 days = 10x
Total No. of books produced is 14x + 16x + 10x = 40x = 1680
x = 42
Therefore, No. of books produced by L, M and N in 3, 6 and 4 days respectively are 2 X 42 X 3 + 4 X 42 X 6 + 5 X 42 X 4 = 2,100.
18. | | If P, Q and R earned Rs. 295 working together on a job, which each can do in 5, 6 and 8 days respectively, what is the share of R? | | (a)Rs. 150 | | (b)Rs. 120 | | (c)Rs. 100 | | (d)Rs. 75 |
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Answer is: DIn one day P, Q and R can do (1/5)th , (1/6)th and (1/8)th of the total work respectively.
The money will be shared in the ratio = 1/5 : 1/6 : 1/8 i.e. 24 : 20 : 15
R's share is (15 X 295)/(24 + 20 + 15) = 75
R's share is Rs. 75
19. | | A house can be painted by 7 men and 2 women in 8 days, if they work for 12 hours a day. Working at the same rate, 6 men and 20 women can do the same job in 4 days. In how many hours can 8 men and 8 women paint the house? | | (a)12 hours | | (b)16 hours | | (c)64 hours | | (d)32 hours |
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Answer is: CLet the amount of work done by 1 man in 1 day for 12 hours be 'm'
and 1 woman in 1 day for 12 hours be 'w'.
Total work done by 7 men and 2 women in 8 days working 12 hours a day is
8(7m + 2w) →(1)
Total work done by 6 men and 20 women in 4 days working 12 hours a day is
4(6m + 20w) →(2)
Equating (1) and (2)
56m + 16w = 24m + 80w
32m = 64w
m = 2w
Total work = 8 {7m + m} = 64
20. | | P and Q can do a certain work together in 12 days, Q and R in 20 days, and P and R in 15 days. P, Q and R start working together. They work for 2 days after which Q leaves. After 10 more days Q rejoins and P leaves. Q works for 2 days along with R and then he leaves. They remaining work is completed by R. In how many days will the work be completed? | | (a)12 days | | (b)20 days | | (c)16 days | | (d)24 days |
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Answer is: CLet the work be completed by P, Q and R alone in p, q and r respectively
so, 12(1/p + 1/q) = 20(1/q + 1/r) = 15(1/p + 1/r)
solving the above equation we get,
1/p = 1/20
1/q = 1/30
1/r = 1/60
P, Q and R can do the work alone in 20, 30 and 60 days respectively.
P works for 12 days, Q works for 4 days and R completes the remaining work in x days.
so, 12/20 + 4/30 + x/60 = 1
(36 + 8 + x)/60 = 1
x = 16
The work will be completed in 16 days.
21. | | A, B and C can do a piece of work in 6, 8 and 10 hours respectively. Find the time taken by A, B and C, working together, to do a work which can be done by C alone in 25 hours. | | (a)629/47 hours | | (b)620/47 hours | | (c)619/47 hours | | (d)618/47 hours |
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Answer is: DIf C can do a work in 10 hours, A and B can do it in 6 and 8 hours respectively.
If C can the work in 25 hours A and B take 6 X 25/10 and 8 X 25/10 hours i.e. 15 hours and 20 hours.
time taken by three of them to do work, which takes C, 25 complete hours, is
1/(1/15 + 1/20 + 1/25) = 300/47 hours = 618/47 hours.
22. | | Three machines P, Q and R can do a piece of work in 7, 9 and 10 days respectively. Due to a problem in P and Q, they are working only at 70% and 90% of their efficiencies respectively. In how many days P, Q and R together can do the work? | | (a)5/3 day | | (b)7/3 days | | (c)8/3 days | | (d)10/3 days |
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Answer is: DAmount of work P can do in a day is 1/7 X 70/100 = (1/10)th
Amount of work Q can do in a day is 1/9 X 90/100 = (1/10)th
Amount of work R can do in a day is (1/10)th
P, Q and R together can do (3/10)th of the total work in a day.
They can complete the work in 1/(3/10) = 10/3 days.
23. | | A can complete a piece of work x in 10 days, B can complete the same work in 20 days and C can complete the same work in 25 days. If they take 40 days to complete a piece of work y, then in how many days C alone can complete the work y? | | (a)65 days | | (b)76 days | | (c)190 days | | (d)95 days |
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Answer is: CA, B and C can complete the work and in 10 days, 20 days and 25 days respectively.
The ratio of efficiency of A, B, C is A : B : C = 1/10 : 1/20 : 1/25 = 10 : 5 : 4
C can do (4/19)th of the work done by A, B and C together.
so, C takes (19/4) times the time taken by A, B and C together.
If A, B and C together can complete a piece of work in 40 days, then C alone complete it in (19/4) X 40 days i.e. 190 days.
24. | | A can do a piece of work in 20 day and B can do the same work in 30 days. They finished the work with the help of C in 8 days. If they earned a total of Rs. 5550, then what is the share of C? | | (a)Rs. 1800 | | (b)Rs. 1850 | | (c)Rs. 1900 | | (d)Rs. 1950 |
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Answer is: BGiven,
A complete the work in 20 days
A completes 1/20 of the work in one day.
B complete the work in 30 days.
B completes 1/30 of the work in one day.
In one day A and B together can do 1/20 + 1/30 = 1/12 of the work in one day.
Given ,
A, B and C together completed the work in 8 days,
so, they can completed 1/8 of the work in one day.
The work done by C in one day = 1/8 - 1/12 = 1/24 of the work.
Employment done by C in 8 days = 8 X 1/24 = 1/3 of the work.
than, share of C = 5550 X 1/3 = Rs. 1850
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