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Q #11
:

Directions: Read the following information to answer the question.

Distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph. While the other man travelled with varying speeds as follows: In first hour his speed was 2 kmph, in the second hour it was 2.5 kmph, in the third hour it was 3 kmph, and so on. When will they meet each other?

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The Let X and Y be the persons who started from A and B respectively.

Midway between A and B means 36 km. From A,   X will take 9 hours to reach the midpoint. In 9 

hours Y will also cover 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 = 36 km. Thus Y will also reach the midpoint at the same time.


Q #12
:

Directions: Read the following information to answer the question.

A man travels form A to B at a speed of x kmph. He then rests at B or x hours. He then travels from B to C at a speed of 2x kmph and rests at C for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to 12 km, the time for which he rested at B could be:

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We are given that AB = BC = CD = 12 km. ∴ time taken to travel AB at a speed of x kmph is (12/x) hours. This is followed by a break of x hours. His speed from C to D is 2(2x) = 4x kmph. Continuing on these lines, we get, [(12/x) + x + (12/2x) + 2x + (12/4x)] = 16 hours. Solving we get x = 3.


Q #13
:

Directions: Read the following information to answer the question.

In a mile race Akshay can be given a start of 128 metres by Bhairav. If Bhairav can given Chinmay a start of 4 metres in a 100 metres dash, then who out of Akshay and Chinmay will win a race of one and half mile, and what will be the final lead given by the winner to the loser? (One mile is 1600 metres).

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When Bhairav (B) covers 1600 m, Akshay (A) covers (1600 - 128) m. So, when B covers (1600/16) = 100 m, A covers (128/16) m = 8 m less. When B covers 100 m, C covers (100 - 4) = 96 m. Thus the ratio in which A and C cover distances is 92 : 96. In 96 m, C gains (96 - 92) = 4 m over A. So in 1.5 miles (i.e. 2400 m), C gains 100 m = (1/16) miles over A.

Q #14
:

Directions: Read the following information to answer the question.

A train X departs from station A at 11.00 a.m. for station B, which is 180 km away. Another train Y departs from station B at the same time. Train X travels at an average speed of 70 km/hr and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km\hr, but has to stop for 15 minutes at station C, which is 60 km away from station B enroute to station A. At what distance from A would they meet?

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Time taken to cover 60 km by train Y = 60/50    = 1 hr 12 min.

Rest = 15 min. Total time = 1 hr 27 min.                Distance from A of train X = 100 km approx.                Remaining distance = 180 – (100 + 60) = 20 km.           

Time taken to meet = [    Distance/Relative Speed]= 20/120 = 1/6 hr.

Distance from A = 70 ×    1/6 = 11 approx.               

Total distance = 100 + 11 = 111 km

 


Q #15
:

Directions: Read the following information to answer the question.

Two persons start, one from point A towards B and the other from B towards A. Distance between A and B is d meters. The person starting from B gives a whistle as soon as he starts and the person starting from A hears the whistle after 10 seconds of his (A) start. Speed of A and B are 2m/s and 1.5m/s respectively. Speed of sound is 330m/s.

What is the distance in metres?

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Since A listens the whistle after 10 seconds, so both the sound of whistle

and person A both have travelled for 10 seconds, therefore the distance

travelled by A = 20 mts and that by sound = 330 × 10 = 3300 m. So the

distance d = 3320 m.