Time and Work
- 'A' can do a piece of work in 2 hours, 'B' can do thrice the work in 8 hours and ‘C’ can do the same work as 'A' in 8 hours. If all of them work together, how long it would take them to complete the work ?
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Efficiency of A = 50% [100/2]
Efficiency of B = 37.5% [100/(8/3)]
Efficiency of C = 12.5% [100/8]
Combined efficiency of A,B and C = 100%Correct Option: A
Efficiency of A = 50% [100/2]
Efficiency of B = 37.5% [100/(8/3)]
Efficiency of C = 12.5% [100/8]
Combined efficiency of A,B and C = 100%
So, they complete the work in 1 hour.
- 12 men and 16 boys can do a piece of work in 5 days while 13 men and 24 boys finish it in 4 days. 5 men and 10 boys will finish it in ?
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(12 men + 16 boys) can do a work in 5 days.
(60 men + 80 boys) can do a work in 1 day.
(13 men + 24 boys) can do a work in 4 days.
(52 men + 96 boys) can do a work in 1 day.
⇒ 60 men + 80 boys = 52 men + 96 boys
8 men = 16 boys and 1 man = 2 boys
Now, 12 men + 16 boys = (12 x 2 + 16) boys
= 40 boys can do the work in 5 daysCorrect Option: A
(12 men + 16 boys) can do a work in 5 days.
(60 men + 80 boys) can do a work in 1 day.
(13 men + 24 boys) can do a work in 4 days.
(52 men + 96 boys) can do a work in 1 day.
⇒ 60 men + 80 boys = 52 men + 96 boys
8 men = 16 boys and 1 man = 2 boys
Now, 12 men + 16 boys = (12 x 2 + 16) boys
= 40 boys can do the work in 5 days
∴ 5 men + 10 boys = [5 x 2 + 10] boys
= 20 boys will take
= (40 x 5)/20 = 10 days
- Ram finishes a work in 7 days. Rahim finish the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working on the last day when work got finished ?
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Three day work or Ram, Rahim and Robert = 1/7 + 1/8 + 1/6
= (24 + 21 + 28)/168 = 73/168
Their six days work = (2 x 73)/168 = 146/168 = 73/84
Now, its Ram's turn to work on seventh day.
∴ 73/84 + 1/7 = 73 + 12/84 = 85/84 > 1
So, Ram will finish the work before the end of day.
Hence, Ram is working for the last day.Correct Option: A
Three day work or Ram, Rahim and Robert = 1/7 + 1/8 + 1/6
= (24 + 21 + 28)/168 = 73/168
Their six days work = (2 x 73)/168 = 146/168 = 73/84
Now, its Ram's turn to work on seventh day.
∴ 73/84 + 1/7 = 73 + 12/84 = 85/84 > 1
So, Ram will finish the work before the end of day.
Hence, Ram is working for the last day.
- A and B can do a piece of work in 72 days, B and C can do it in 120 days, A and C can do it in 90 days. In what time can A alone do it ?
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Combined efficiency of A and B = 1/72 ....(i)
Combined efficiency of B and C = 1/120 ....(ii)
Combined efficiency of A and C = 1/90 ....(iii)
On adding Eqs. (i), (ii) and (iii), we get
2(A + B + C) = 1/72 + 1/120 + 1/90 = (5 + 3 + 4)/360
= 12 / 360 = 1 / 30
⇒ A + B + C = 1/60 .....(iv)
i.e Combined efficiency is 1/60 or we can say together A, B and C can complete the work in 60 days.Correct Option: D
Combined efficiency of A and B = 1/72 ....(i)
Combined efficiency of B and C = 1/120 ....(ii)
Combined efficiency of A and C = 1/90 ....(iii)
On adding Eqs. (i), (ii) and (iii), we get
2(A + B + C) = 1/72 + 1/120 + 1/90 = (5 + 3 + 4)/360
= 12 / 360 = 1 / 30
⇒ A + B + C = 1/60 .....(iv)
i.e Combined efficiency is 1/60 or we can say together A, B and C can complete the work in 60 days.
On subtracting Eq. (ii)from Eq. (iv), we get
Efficiency of A = Combined efficiency of A, B and C - Combined efficiency of B and C
= 1/60 - 1/120 = 1/120
Hence, A alone can do it in 120 days
- A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. In how many days, B alone will be able to complete the same work ?
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In this question, A and B did the work for 35 days to complete it. A can complete the work in 60 days.
So, A did/A can + B did/B can = 1
⇒ 35/60 + 35/x = 1Correct Option: B
In this question, A and B did the work for 35 days to complete it. A can complete the work in 60 days.
So, A did/A can + B did/B can = 1
⇒ 35/60 + 35/x = 1
⇒ x = 84 days
