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31. Two men A and B start from a place P walking at 4 km and 4.5 km per hour respectively. How many km will they be apart at the end of 4 hours, if they walk in same direction?
  A.  1 km
  B.  5 km
  C.  2 km
  D.  4 km
     
   
View Answer

Shortcut:
If two persons X and Y start from a place walking at a km/hr and b km/hr respectively, at the end of t hours, when they are moving in same direction and a < b, they will be (b − a)t km apart.
Here, a = 4, b = 4.5, t = 4 hour
Using these values in the shortcut, we get:
Required distance = (4.5 − 4) x 4 = 0.5 x 4 = 2.0
Hence, they will 2 km apart from each other.

32. One man takes 100 steps a minute, each 10 decimetres long, another walks 7 km/hr, if they start together, how soon will one of them be 50 metres ahead to the other?
  A.  6 minutes
  B.  5 minutes
  C.  2 minutes
  D.  3 minutes
     
   
View Answer

Shortcut:
If two persons X and Y start from a place walking at a km/hr and b km/hr respectively, at the end of t hours, when they are moving in same direction and a < b, they will be (b − a)t km apart.
100 steps = 10 x 100 = 1000 dm = 100 m
Speed of the first = 100 m/minute =
100 / 60
=
5 / 3
m/sec
Converting m/sec into km/hr
5 / 3
x
18 / 5
= 6 km/hr
Here, a = 6, b = 7, t = ?
Using these values in the shortcut, we get:
Required distance = (7 − 6) x t
50 / 1000
x 60 = (7 − 6) x t
t = 3 min
Hence, they will 50 m apart from each other in 3 minutes.

33. Two men A and B start form a place P walking at 4 km and 4.5 km/hr respectively. How many km will they be apart at the end of 4 hour, if they walk in the opposite directions?
  A.  34 km
  B.  40 km
  C.  24 km
  D.  38 km
     
   
View Answer

Shortcut:
If two persons X and Y start from a place walking at a km/hr and b km/hr respectively, at the end of t hours, when they are moving in opposite direction, they will be (a + b)t km apart.
Here, a = 4, b = 4.5, t = 4
Using these values in the shortcut, we get:
Required distance = (4 + 4.5) x 4 = 8.5 x 4 = 34
Hence, they will 34 km apart from each other in 4 hours.

34. Two men A and B walk from X to Y, a distance of 33 km, at 5 and 6 km an hour respectively, B reaches Y, returns immediately and meets A at Z. Find the distance from X to Z.
  A.  15 km
  B.  30 km
  C.  25 km
  D.  33 km
     
   
View Answer

Shortcut:
If two persons X and Y start walking from A to B, a distance of 'K' km, at the speed of a km/hr and b km/hr respectively. If Y reaches B, returns immediately and meets X at M, then the distance travelled by X (or distance from X to M) is 2K
a / a + b
km and the distance travelled by Y (or AB + BM) is 2K
b / a + b
km.
Here, K = 33, a = 5, b = 6
Using these values in the shortcut, we get:
Required distance = 2 x 33 x
5 / 5 + 6

= 2 x 33 x
5 / 11
= 2 x 3 x 5 = 30
Hence, the distance from X to Z is 30 km.

35. A man sets out to cycle from Delhi to Noida, and at the same time another man starts from Noida to cycle to Delhi. After passing each other they complete their journeys in 16 and 25 hours respectively. At what rate does the second man cycle if the first cycle at 15 km/hr.
  A.  Second man's rate: 12 km/hr
  B.  Second man's rate: 13 km/hr
  C.  Second man's rate: 09 km/hr
  D.  Second man's rate: 12 km/hr
     
   
View Answer

Shortcut:
If two persons X and Y start at the same time in opposite directions from two points and after passing each other they complete the journeys in 'm' and 'n' hours respectively then X's speed : Y's speed = √n : √m Here, m = 16, n = 25
Using these values in the shortcut, we get:
1st man speed / 2nd man speed
=
√25 / √16

1st man speed / 2nd man speed
=
5 / 4

∴ second man's rate =
4 / 5
x 1st man speed
=
4 / 5
x 15 = 4 x 3 = 12
Hence, the second man cycle rate is 12 km/hr.

36. Two guns were fired from the same place at an interval of 6 minutes but a person in a train approaching the place hears the second report 5 minutes 30 seconds after the first. Find the speed of the train, supposing that sound travels at 330 metres/second.
  A.  108 km/hr
  B.  100 km/hr
  C.  112 km/hr
  D.  105 km/hr
     
   
View Answer

Shortcut:
If two guns were fired from the same place at an interval of t1 minutes but a person in a train approaching the place hears the second report t2 minutes after the first, then the speed of the train, supposing that soujd travels at 330 metres per second is 1188 x
t1 − t2 / t2
km/hr
t2 = 5 minutes 30 seconds = 5 x 60 + 30 = 330 seconds or 5.5 minutes
Here, t1 = 6, t2 = 5.5
Using these values in the shortcut, we get:
Required Speed = 1188 x
6 − 5.5 / 5.5

= 1188 x
0.5 / 5.5
= 1188 x
5 / 55
= 1188 x
1 / 11
= 108
Hence, the speed of the train is 108 km/hr.

37. Two boys cover the same distance at the rate of 10 km and 12 km per hours respectively. Find the distance travelled when one takes 15 minutes longer than the other.
  A.  16 km
  B.  12 km
  C.  15 km
  D.  10 km
     
   
View Answer

Shortcut:
If the two runners X and Y cover the same distance at the rate of a km/hr and b km/hr respectively, then the distance travelled, when X takes t hours longer than Y, is
a x b x t / b − a
km
Here, a = 10, b = 12, t = 15 or
15 / 60
or
1 / 4
hours
Using these values in the shortcut, we get:
Required distance =
10 x 12 x 1/4 / 12 − 10

=
10 x 3 / 2
= 5 x 3 = 15
Hence, the distance is 15 km.

38. Two cars run to a place at the speeds of 15 km/hr and 40 km/hr respectively. If the second car takes 10 hours less than the first for the journey, find the length of the journey.
  A.  265 km
  B.  240 km
  C.  210 km
  D.  200 km
     
   
View Answer

Shortcut:
If the two runners X and Y cover the same distance at the rate of a km/hr and b km/hr respectively, then the distance travelled, when X takes t hours longer than Y, is
a x b x t / b − a
km
Here, a = 15, b = 40, t = 10
Using these values in the shortcut, we get:
Required distance =
15 x 40 x 10 / 40 − 15

=
15 x 40 x 10 / 25
= 3 x 40 x 2 = 240
Hence, the distance is 240 km.

39. A man walks from X to Y and retruns in a certain time at the rate of 3
1 / 2
km/hr. But if he had walked from X to Y at the rate of 3 km/hr and return from Y to X at the rate of 4 km/hr, he would have taken 15 minutes longer. Find the distance between X and Y.
  A.  14 km
  B.  7 km
  C.  8 km
  D.  7 km
     
   
View Answer

Shortcut:
If the two runners X and Y cover the same distance at the rate of a km/hr and b km/hr respectively, then the distance travelled, when X takes t hours longer than Y, is
a x b x t / b − a
km
Man speed in 1st case = 5
1 / 2
or
11 / 2
km/hr
Man's average speed in the second case =
2 x 3 x 4 / 3 + 4
=
24 / 7

Here, a =
7 / 2
, b =
24 / 7
, t = 5 minutes or
5 / 60
or
1 / 12

Using these values in the shortcut, we get:
Required distance =
7/2 x 24/7 x 1/12 / 7/2 − 24/7

=
1 / (49 − 48)/14
=
14 / 1
= 14
2XY = 14
XY =
14 / 2
= 7
Hence, the distance is 7 km.

40. A car starts form X for Y travelling 30 km/hr. 3
1 / 2
hours later another car starts from X and travelling at the rate of 40 km/hr reaches Y 4
1 / 2
hrs before the first car. Find the distance form X to Y.
  A.  960 km
  B.  960 km
  C.  960 km
  D.  960 km
     
   
View Answer

Shortcut:
If the two runners X and Y cover the same distance at the rate of a km/hr and b km/hr respectively, then the distance travelled, when X takes t hours longer than Y, is
a x b x t / b − a
km
t = 3
1 / 2
+ 4
1 / 2
=
7 / 2
+
9 / 2
=
16 / 2
= 8
Here, a = 30, b = 40, t = 8
Using these values in the shortcut, we get:
Required distance =
30 x 40 x 8 / 40 − 30

=
30 x 40 x 8 / 10
= 3 x 40 x 8 = 960
Hence, the distance is 960 km.

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