Quant Boosters  Maneesh  Set 2

Once the minute hand and hour hand are together, minute hand starts increasing the gap between the hour hand itself by 11/2 degree every minute. Therefore when it has increased the gap by 360 degree it again meets the hour hand. Time taken to increase the gap by 360 degree it again meets the hour hand.
Time taken to increase the gap by 360 degree = 360 / (11/2) = 720/11 = 65 5/11 minutes.
Therefore minute hand and hour hand meets in every 65 5/11 minutes.

Q2) Rahul starts a trip when the hands of clock are together between 8am and 9am.He arrives his destination between 2pm and 3pm when the hands are exactly 180 degree apart. How long did the trip take?

At 8am distance between minute hand and hour hand is 240 degree.
It takes minute hand 240/(11/2) = 480/11 = 43 7/11 minutes to catch up with hour hand. Therefore at 43 7/11 minutes past 8.00 the two hands are together.
At 2 pm the distance between minute hand and hour hand is 60 degree. The total relative distance minute hand needs to travel is 240 degree with respect to hour hand.
Therefore time taken = 240/ (11/2) = 480/11 = 43 7/11 minutes.
Therefore at 43 7/11 minutes past 2.00 the two hands are 180 degree apart.
Total time taken = 6 hours.

Q3) Rahul left his house between 2 o clock and 3 o clock in the afternoon. He returned home between 5 o clock and 6 o clock in the evening and noticed that the hour hand and minute hand interchanged their position with what there when he went out. At what time did he return?

Let angle between minute hand and hour hand be x.
So hour hand moves x degree, minute hand moves 1080x degree
When hour hand moves x degree minute hand moves 12x degree
12x = 1080x
13x = 1080 = > x = 1080/13
Now we need to find when angle will be 1080/13 between 5 and 6
30*5 – 11M/2 = 1080/13
M = 1740/143
So time is 1740/143 minutes past 5.

Q4) Local trains leave a station at an interval of 15 minutes at a speed of 16 kmph. A man moving from opposite direction meets the train at an interval of 12 minutes. What is the speed of man?

Let speed of Man is S
Relative speed = 16+S
15 minutes = 1/4 hour
Trains are 16/4 = 4 km apart
So 4 = (16+S) * 1/5
S = 2016 = 4 kmph

Q5) Ravi takes 40 seconds to walk up on an escalator which is moving upwards but he takes 60 seconds to walk up on an escalator which is moving downwards. How much time will he take to walk up if the escalator is not moving?

Let speed of Ravi r and speed of escalator is x
When both are moving up, effective speed (r+x)
When escalator moving down, Ravi moving up effective speed rx
When escalator not moving his speed r
Speeds (rx), r and (r+x) are in A P
so time taken when escalator is not moving will be HM of other two time.
Time taken when escalator is not moving = 24060/100 = 48 seconds

Q6) Ravi takes 60 seconds on an escalator which is moving down when he walks down but takes 40 seconds when he runs down. He takes 20 steps when he is walking whereas he takes 30 steps when he is running. What is the total number of steps in escalator ?

Let speed of escalator x steps/second
Distance covered by Ravi is same whether he walks or runs
20 + 60x = 30 + 40x
20x = 10
x = 1/2 steps/second
total number of steps = 20 + 60 * 1/2 = 50 steps

Q7) Ravi and Rakesh are climbing on a moving escalator that is going up. Ravi takes 10 seconds to reach the top but Rakesh takes 8 seconds to reach the top. Rakesh takes 4 steps whereas Ravi can take only 3 steps in one second. What is the total number of steps in Escalator?

Speed of escalator x steps/second
Distance covered by both is same
10(3+x) = 8(4+x)
x = 1 step/second
Number of steps = 10 * 4 = 40 steps.

Q8) Two swimmers started simultaneously from the beach to the south and other to the east. Two hours later the distance between them turned out to be 100 KM. Find the speed of faster swimmer knowing that speed of one of them was 75% of speed of other?

Let speed s. Distance travelled in 2 hours 2s
speed 3s/4 = > distance travelled in 2 hours = 3s/2
it will form a right angled triangle.
(3s/2)^2 + (2s)^2 = 100^2
9s^2/4 + 4s^2 = 100^2
S = 40KMPH

Q9) Two men A and B run a 4 km race on a circular course of ¼ KM. If their speeds are in the ratio of 5:4. How often does the winner pass the other?

When a completes 5 rounds B completes 4 rounds
So A will overtake B when he completes 5 round = > 5 * 1/4 = 5/4 km
So there are three 5/4 km in 4 KM
So A will pass B in 3 times.

Q10) The Howrah –puri express can move at 45 km/hr without its rake, and the speed is diminished by a constant that varies as the square root of the number of wagons attatched.If its known with 9 wagons the speed is 30 KM/HR what’s greatest number of wagons with which the train can just move?

S1/S2 = root ((W1/W2))
where S is change in speed and w is number of wagons
S1 = 4530 = 15
W1 = 9
S2 = 450 = 45
15/45 = 3/ROOT(W2)
W2 = 81
So if 81 wagons are there then train wont move
so answer is 80

Q11) A watch which gains uniformly is 2 minutes slow at noon on Sunday and is 4 minutes 48 seconds fast at 2 PM on the following Sunday. When was it correct?