Time and Work
- A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C and do it in 90 days. In what time can A alone do it?
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(A + B )'s 1 day ' s work = 1/72
(B + c)'s 1 day' s work = 1/120
(A + C)'s 1 day's work = 1/90
2(A + B + C)'s 1 days work = 1/72 + 1/120 + 1/90
∴ ( A + B + C )'s 1 day's work (5 + 3 + 4)/(360 x 2) = 12/(360 x 2) = 1/60
∴ A's 1 day's work = (A + B + C) 's 1 day's work - (B + C)'s 1 day's workCorrect Option: C
(A + B )'s 1 day ' s work = 1/72
(B + c)'s 1 day' s work = 1/120
(A + C)'s 1 day's work = 1/90
2(A + B + C)'s 1 days work = 1/72 + 1/120 + 1/90
∴ ( A + B + C )'s 1 day's work (5 + 3 + 4)/(360 x 2) = 12/(360 x 2) = 1/60
∴ A's 1 day's work = (A + B + C) 's 1 day's work - (B + C)'s 1 day's work
= 1/60 - 1/120 = (2 - 1)/120 = 1/120
∴ A alone can finish the work in 120 days.
- A can do a piece of work in 5 hours, B in 9 hours and C in 15 hours. If C could work with them for 1 hour only the time taken by A and B together to complete the work is ?
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∵ (1/5 + 1/9 + 1/15) = 17/45 work is finished in 1 hour
∴ Remaining work = 1 - 17/45 = 28/45
⇒ (A + B)'s 1 hour's work = 1/5 + 1/9 = 14/45Correct Option: A
∵ (1/5 + 1/9 + 1/15) = 17/45 work is finished in 1 hour
∴ Remaining work = 1 - 17/45 = 28/45
⇒ (A + B)'s 1 hour's work = 1/5 + 1/9 = 14/45
14/45 work is done by (A and B) in 1 hour
28/45 work will be done by A and B in (45/14) x (28/45) = 2 hours
- 25 men reap a field in 20 days. When should 15 men leave the work, if the whole field is to be reaped in 371/2 day after they leave the work ?
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25 men reap the field in 20 days
∴ 10 men can reap the feild in (20 x 25)/ 10 = 50 days.
When 15 men leave the work, 10 men remain and they can reap in 371/2 days
= (371/2)/ 50 = 3/4 of the fieldCorrect Option: C
25 men reap the field in 20 days
∴ 10 men can reap the feild in (20 x 25)/ 10 = 50 days.
When 15 men leave the work, 10 men remain and they can reap in 371/2 days
= (371/2)/ 50 = 3/4 of the field
Hence, all men must work till (1 - 3/4) = 1/4 of the field is reaped in 20/4 = 5 days.
- A can do a piece of work in 24 days while B alone can do it in 16 days. But with the help of C, they finish the work in 8 days. C alone can do the work in ?
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∵ C's 1 day's work
= [( A + B + C)'s 1 day's work] - [(A + B)'s 1 day's work]
= [1/8 - (1/24 + 1/16)] = (1/8 - 5/48) = 1/48Correct Option: D
∵ C's 1 day's work
= [( A + B + C)'s 1 day's work] - [(A + B)'s 1 day's work]
= [1/8 - (1/24 + 1/16)] = (1/8 - 5/48) = 1/48
∴ C alone can do it in 48 days.
- A and B can do a piece of work in 18 days. B and C in 24 days, C and A in 36 days. Find the time in which A, B and C working together can finish the work.
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(A+ B )' s 1 day ' s work = 1/18
(B +C )'s 1 day ' s work = 1/24
(C + A) 's 1 day 's work = 1/36
From Eqs. (i), (ii) and (iii), we get
2(A + B + C)' s 1 day 's work = 1/18 + 1/24 + 1/36Correct Option: B
(A+ B )' s 1 day ' s work = 1/18
(B +C )'s 1 day ' s work = 1/24
(C + A) 's 1 day 's work = 1/36
From Eqs. (i), (ii) and (iii), we get
2(A + B + C)' s 1 day 's work = 1/18 + 1/24 + 1/36
(A + B + C)'s 1 day's work = (4 + 3 + 2)/(72 x 2)
= 9/(72 x 2) = 1/16
∴ (A + B + C) can complete the work in 16 days
