Time & Work - Previous Year IPM/BBA Questions
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Amisha can complete a particular task In twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be.
Answer: 24
Text Explanation :
Let the efficiency of Amish be 2 units/day.
If she can do the entire work in 20 days.
⇒ Total work to be done = 2 × 20 = 40 units.
Now, she works with full efficiency for first 4 days and with half efficiency for another 12 days.
∴ Work done by Amisha = 2 × 4 + 1 × 12 = 20 units.
⇒ Amisha's co-worker completed the remaining (40 - 20 =) 20 units of work in the last 12 days.
Hence, to complete the entire 40 units of work the co-worker will take 24 days.
Hence, 24.
Workspace:
There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for the water tank (initially full) to become empty if T2 is opened while T1 is closed is
Answer: 60
Text Explanation :
T1 alone can empty the tank in 30 minutes.
T1 and T2 together can empty the tank in 20 minutes.
Let the time taken by T2 alone is t minutes.
⇒ + =
⇒ t = 60 minutes.
Hence, 60.
Workspace:
Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast at the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is
- (a)
(√33 + 4)/3
- (b)
(√33 + 3)/3
- (c)
(√33 + 6)/5
- (d)
(√33 + 7)/3
Answer: Option A
Text Explanation :
Let the time taken by the first worker be x hours.
∴ Time taken by the second worker = x + 1 hours.
∴ Time taken by the third worker = 2x hours.
Together they take 1 hour to complete the task.
⇒ =
⇒ =
⇒ 3(x + 1) + 2x = 2x × (x + 1)
⇒ 5x + 3 = 2x2 + 2x
⇒ 2x2 - 3x - 3 = 0
⇒ x = =
We will accept only +ve value.
∴ x =
⇒ Required average = = =
Hence, option (a).
Workspace: