Time and Work
- 2 men and 3 women finish 25% of the work in 4 days, while 6 men and 14 women can finish the whole work in 5 days, In how many days will 20 women finish it?
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8M + 12W = 4 days (whole work)
⇒ 32M + 48W = 1 day ................ (1)
Again 6M + 14W = 5 days
⇒ 30M + 70W = 1 day ................(2)Correct Option: A
8M + 12W = 4 days (whole work)
⇒ 32M + 48W = 1 day ................ (1)
Again 6M + 14W = 5 days
⇒ 30M + 70W = 1 day ................(2)
From eq. (1) and (2)
32M + 48W = 30M +70W
⇒ 2M = 22W
⇒ 1M = 11W
Now, 30M + 70W = 1 day
(30 X 11 X 70)W = 1 day
Therefore 400W requires 1 day to complete the whole work.
Thus 20W needs 20 days to complete the whole work.
- A and B can do a piece of work in 12 days, B and C can do it in 15 days and C and A can do the same work in 20 days. Find the number of days in which A alone can do the same job ?
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Work done by A and B in one day = 1/12
Work done by B and C in one day = 1/15
Work done by C and A is one day = 1/20
On adding all these,
2(A + B + C)'s work of one day = 1/12 + 1/15 +1/20 = 1/5
⇒ (A + B + C)'s one day work = 1/10
∴ A' s one day work = (A + B + C)'s one day work - (B + C )'s one day workCorrect Option: B
Work done by A and B in one day = 1/12
Work done by B and C in one day = 1/15
Work done by C and A is one day = 1/20
On adding all these,
2(A + B + C)'s work of one day = 1/12 + 1/15 +1/20 = 1/5
⇒ (A + B + C)'s one day work = 1/10
∴ A' s one day work = (A + B + C)'s one day work - (B + C )'s one day work
⇒ A's one day work 1/10 - 1/15 = 1/30
Hence, A can do this work in 30 days.
- A leak in the bottom of a tank can empty the full tank in 6 h. An inlet pipe fills water at the rate of 4 L in a min. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 h. Find the capacity of the tank ?
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Efficiency of the leak = 1/6
Combined efficiency of leak and inlet pipe
So, efficiency of inlet pipe = 1/6 - 1/8 = (4 - 3)/24 = 1/24
Inlet pipe can fill the tank in 24 h, at rate of 4 L/min.Correct Option: D
Efficiency of the leak = 1/6
Combined efficiency of leak and inlet pipe
So, efficiency of inlet pipe = 1/6 - 1/8 = (4 - 3)/24 = 1/24
Inlet pipe can fill the tank in 24 h, at rate of 4 L/min.
∴ Capacity = 24 x 60 x 4 = 5760 L
- A man, a women and a boy can do a job in 3, 4 and 12 days , respectively. How many boys must assist one man and one women to complete the job in one and a half days ?
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Portion of work completed by one man in 11/2 days.
i.e., 3/2 days = 3/(2 x 3) = 1/2
Portion of work completed by one women in 11/2 days.
i.e., 3/2 days = 3/(2 x 4) = 3/8
∴ Portion of work completed by boys = 1 - (1/2 + 3/8) = 1/8
Now, portion of work completed by each boy in 3/2 days = 3/(2 x 12) = 1/8Correct Option: D
Portion of work completed by one man in 11/2 days.
i.e., 3/2 days = 3/(2 x 3) = 1/2
Portion of work completed by one women in 11/2 days.
i.e., 3/2 days = 3/(2 x 4) = 3/8
∴ Portion of work completed by boys = 1 - (1/2 + 3/8) = 1/8
Now, portion of work completed by each boy in 3/2 days = 3/(2 x 12) = 1/8
Hence, only one boys would be required.
- Pipes A and B can fill a tank in 20 h and 30 h, respectively and pipe C can empty the full tank in 40 h. If all the pipes are opened together, how much time will be needed to make the tank full ?
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Net part filed in 1 h = (1/20 + 1/30 - 1/40) = 7/120
Correct Option: B
Net part filed in 1 h = (1/20 + 1/30 - 1/40) = 7/120
Hence, the tank will be full in 120/7 = 171/7 h
