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# CAT Problems on Time and Work PDF:

Question 1:
A flight starts from Delhi at 9:00 am local time and reaches Dubai at 1 am local time. The same flight starts from Dubai at 3pm local time and reaches Delhi and 3 am local time. If the flight undertook both the journies at the same speed, find the time difference between Dubai and Delhi?

a) 3 hours
b) 1.5 hours
c) 2 hours
d) 2.5 hours

Question 2: What is the minor angle made by the minute hand and hour hand when the time is 3:48 PM?

a) 176
b) 174
c) 172
d) 170

Question 3: A, B, C and D are four men. A does a piece of work four times faster than B. B does the same work four times faster than C, who does the same piece of work four times faster than D. Three of the four men take 21 days to complete a piece of work while another group of three men take 81 days to complete the same piece of work. Find the group of people who take 21 days to complete the piece of work.

a) A, B, C
b) A, B, D
c) A, C, D
d) B, C, D

Question 4: P and Q start from X and Y respectively at 10 AM and travel towards Y and X. If P reaches Y at 2 PM and Q reaches X at 4 PM, at what time do they meet?

a) 12:18 PM
b) 12:20 PM
c) 12:24 PM
d) 12:15 PM

Question 5: X, Y and Z ran a 50 m race. The time taken by X was recorded by watch W1 and the time taken by Y and Z was recorded by watch W2. The time taken by X, Y and Z to complete the race according to the respective watches used was 5, 6 and 3 seconds respectively. W2 is a faulty clock and loses time uniformly. If X beats Y by 10 m, what was the speed of Z during the race?

a) None
b) None
c) None
d) None

Solutions:

Let Delhi be x hours ahead of Dubai.
Time taken ignoring time difference = 24 hours – (9am – 1am) = 16 hours
Actual time taken = 16 + x
Time taken from Dubai to Delhi ignoring time difference = 3 am – 3 pm = 12 hours
Actual time taken = 12 – x
As the same distance is covered in each case at same speed, time taken would be the same.
Hence, 16 + x = 12 – x
x = -2 hours
Hence, Dubai is ahead of Delhi by 2 hours.

Each minute is equal to 360/60 = 6°
48 minutes => 48 * 6 = 288°
Hour hand covered 3.8 hours.
Each hour = 360/12 = 30°
3.8 hours => 3.8 * 30 = 114°
Hence, the minor angle made = 288°
– 114°
= 174°

Let the work done by D in a day be x.
=> Work done by C in a day = 4x
=> Work done by B in a day = 16x
=> Work done by A in a day = 64x
Work done by A, B and C in a day = 84x
Work done by A, B and D in a day = 81x
Work done by A, C and D in a day = 69x
Work done by B, C and D in a day = 21x
We can infer that the group that takes 21 days to complete the work is A, B and D and the group that takes 81 days to complete the work is B, C and D.

P takes 4 hours and Q takes 6 hours .
Ratio of speed of P and Q = 3:2
Let the speed of P and Q be 3km/hr and 2km/hr and XY = 12km. Let x be the distance traveled by P to meet Q. Thus, the distance traveled by Q = 12 – x.
Since, the time taken to meet each other is same,
x/3 = (12-x)/2
x = 7.2 km
Time taken = 7.2/3 = 2.4 hours = 2 hours + 40% of 60 minutes = 2 hours + 24 minutes.