TIME AND WORK
- Two pipes A and B can independently fill a tank completely in 20 and 30 minutes respectively. If both the pipes are opened simultaneously, how much time will they take to fill the tank completely ?(2015)
(A) 10 minutes
(B) 12 minutes
(C) 15 minutes
(D) 25 minutes
Answer-B
Let's calculate the rates at which pipes A and B can fill the tank.
Pipe A can fill the tank in 20 minutes, so its rate is 1/20 tanks per minute.
Pipe B can fill the tank in 30 minutes, so its rate is 1/30 tanks per minute.
When both pipes A and B are opened simultaneously, their rates add up:
Combined rate = Rate of pipe A + Rate of pipe B
Combined rate = 1/20 + 1/30
Combined rate = (3/60 + 2/60)
Combined rate = 5/60
Combined rate = 1/12 tanks per minute
This means that when both pipes A and B are opened together, they fill 1/12 of the tank per minute
To find the time taken to fill the tank completely, we need to divide the total tank capacity by the combined rate:
Time = Tank capacity / Combined rate
Time = 1 / (1/12)
Time = 12 minutes
Therefore, when both pipes A and B are opened simultaneously, they will take 12 minutes to fill the tank completely.
The correct answer is (b) 12 minutes.
- Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?(2016)
(A) 6 days
(B) 8 days
(C) 10 days
(D) 11 days
Answer-C
Let's assume that the job requires 100 units of work.
As per the question, Ram and Shyam together complete 60% of it in 4 days.
So, the amount of work completed by both of them in one day = 60/4 = 15 units.
Now, as Ram takes leave, only Shyam works for 8 more days to complete the remaining 40% of the job.
So, the amount of work completed by Shyam in one day = 40/8 = 5 units.
Thus, the amount of work done by Ram in one day = 15 - 5 = 10 units.
Therefore, Ram alone can complete the job in 100/10 = 10 days.
- W can do 25% of a work in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?(2016)
(A) W
(B) X
(C) Y
(D) Z
Answer-D
Let's calculate the rate at which each person completes the work.
W can do 25% of the work in 30 days, so their daily rate is 25% / 30 = 1/120 of the work per day.
X can do 1/4 of the work in 10 days, so their daily rate is 1/4 / 10 = 1/40 of the work per day.
Y can do 40% of the work in 40 days, so their daily rate is 40% / 40 = 1/100 of the work per day.
Z can do 1/3 of the work in 13 days, so their daily rate is 1/3 / 13 = 1/39 of the work per day.
To determine who will complete the work first, we need to find the person with the highest daily rate.
Comparing the rates:
W: 1/120 of the work per day
X: 1/40 of the work per day
Y: 1/100 of the work per day
Z: 1/39 of the work per day
It is clear that Z has the highest daily rate among all the people.
Therefore, Z will complete the work first.
The correct answer is (b) X.
- A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?(2020)
(A) 6
(B) 10
(C) 8
(D) 12
Answer-A
Let's calculate the rates at which person X and person Y can complete the work.
Person X can complete 20% of the work in 8 days, so their daily rate is 20% / 8 = 2.5% of the work per day.
Person Y can complete 25% of the work in 6 days, so their daily rate is 25% / 6 = 4.1667% of the work per day.
When they work together, their rates add up:
Combined rate = Rate of person X + Rate of person Y
Combined rate = 2.5% + 4.1667%
Combined rate = 6.6667% of the work per day
To find the number of days required to complete 40% of the work, we need to divide the total work by the combined rate:
Time = Work / Combined rate
Time = 40% / 6.6667%
Time = (40 / 100) / (6.6667 / 100)
Time = 40 / 6.6667
Time ≈ 6
Therefore, when person X and person Y work together, it will take approximately 6 days to complete 40% of the work.
The correct answer is (a) 6.
- A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50% ?(2021)
(A) 24
(B) 21
(C) 18
(D) 15
Answer-D
Let's calculate the rate at which the man completes the job.
The man completes 7/8 of the job in 21 days. This means that his daily rate is (7/8) / 21 = 1/24 of the job per day.
Now, let's consider the increased quantum of work. If the quantum of work is increased by 50%, it means the man needs to complete 1 + 50% = 1.5 times the original job.
To find the number of days it will take him to finish the increased job, we can calculate the rate required:
Required rate = (1.5) / x, where x is the number of days.
Now, let's set up a proportion:
(1/24) = (1.5) / x
To solve for x, we can cross-multiply:
1/24 * x = 1.5
x = 1.5 * 24
x = 36
Therefore, it will take the man an additional 36 - 21 = 15 days to finish the job if the quantum of work is increased by 50%.
The correct answer is (d) 15.
- 24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?(2022)
(A) 30 days
(B) More than 30 days
(C) Less than 30 days or more than 30 days
(D) Data is inadequate to draw any conclusion
Answer-D
