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41. A carriage driving in a fog passed Raju who was walking at the rate of 4 km/hr in the same direction. Raju could see the carriage for 3 minutes and it was visible to him upto a distance of 200 m. What was the speed of the carriage?
  A.  8 km/hr
  B.  5 km/hr
  C.  7 km/hr
  D.  10 km/hr
     
   
View Answer

Shortcut:
A carriage driving in a fog passed a man who was walking at the rate of a km/hr in the same direction. If he could see the carriage for t hours and it was visible to him upto a distance of 'n' km, then the distance travelled by the carriage in t hours is (at + n) metres and speed of the carriage is
a +
n / t
km/hr
t = 3 min =
3 / 60
=
1 / 20
hrs
n = 200, m =
200 / 1000
=
1 / 5
km
Here, a = 4, t =
1 / 20
, n =
1 / 5

Using these values in the shortcut, we get:
Required speed = 4 +
1/5 / 1/20

= 4 +
20 / 5
= 4 + 4 = 8
Hence, the speed is 8 km/hr.

42. A carriage driving in a fog passed a man who was walking at the rate of 1
1 / 2
km/hr in the same direction. He could see the carriage for 2 minutes and it was visible to him upto a distance of 50 metres. What was the speed of the carriage?
  A.  5 km/hr
  B.  3 km/hr
  C.  7 km/hr
  D.  8 km/hr
     
   
View Answer

Shortcut:
A carriage driving in a fog passed a man who was walking at the rate of a km/hr in the same direction. If he could see the carriage for t hours and it was visible to him upto a distance of 'n' km, then the distance travelled by the carriage in t hours is (at + n) metres and speed of the carriage is a +
n / t
km/hr
a = 1
1 / 2
=
3 / 2

t = 2 min =
2 / 60
1 / 30
hrs
n = 50 m = 50/1000 =
1 / 20
km
Here, a =
3 / 2
, t =
1 / 30
, n =
1 / 20

Using these values in the shortcut, we get:
Required speed =
3 / 2
+
1/20 / 1/30

=
3 / 2
+
30 / 20
=
3 / 2
+
3 / 2
=
6 / 2
= 3
Hence, the speed is 3 km/hr.

43. A carriage driving in a fog passed a man who was walking at the rate of 10 km/hr in the same direction. He could see the carriage for 12 minutes and it was visible to him upto a distance of 250 metres. What was the speed of the carriage?
  A.  9
5 / 4
km/hr
  B.  11
1 / 4
km/hr
  C.  13
7 / 4
km/hr
  D.  12
3 / 4
km/hr
     
   
View Answer

Shortcut:
A carriage driving in a fog passed a man who was walking at the rate of a km/hr in the same direction. If he could see the carriage for t hours and it was visible to him upto a distance of 'n' km, then the distance travelled by the carriage in t hours is (at + n) metres and speed of the carriage is a +
n / t
km/hr
t = 12 min =
12 / 60
=
1 / 5
hrs
n = 250 m =
250 / 1000
=
1 / 4
km
Here, a = 10, t =
1 / 5
, n =
1 / 4

Using these values in the shortcut, we get:
Required speed = 10 +
1/4 / 1/5

= 10 +
5 / 4
=
40 + 5 / 4
=
45 / 4
= 11
1 / 4

Hence, the speed is 11
1 / 4
km/hr.

44. A carriage driving in a fog passed a man who was walking at the rate of 3 km/hr in the same direction. He could see the carriage for 4 minutes and it was visible to him upto a distance of 200 metres. What was the speed of the carriage?
  A.  6 km/hr
  B.  3 km/hr
  C.  9 km/hr
  D.  5 km/hr
     
   
View Answer

Shortcut:
A carriage driving in a fog passed a man who was walking at the rate of a km/hr in the same direction. If he could see the carriage for t hours and it was visible to him upto a distance of 'n' km, then the distance travelled by the carriage in t hours is (at + n) metres and speed of the carriage is a +
n / t
km/hr
t = 4 min =
4 / 60
=
1 / 15
hrs
n = 200 m =
200 / 1000
=
1 / 5
km
Here, a = 3, t =
1 / 15
, n =
1 / 5

Using these values in the shortcut, we get:
Required speed = 3 +
1/5 / 1/15

= 3 +
15 / 5
= 3 + 3 = 6
Hence, the speed is 6 km/hr.

45. A carriage driving in a fog passed a man who was walking at the rate of 10 km/hr in the same direction. He could see the carriage for 20 minutes and it was visible to him upto a distance of 250 metres. What was the speed of the carriage?
  A.  9
7 / 4
km/hr
  B.  10
3 / 4
km/hr
  C.  14
3 / 5
km/hr
  D.  11
5 / 4
km/hr
     
   
View Answer

Shortcut:
A carriage driving in a fog passed a man who was walking at the rate of a km/hr in the same direction. If he could see the carriage for t hours and it was visible to him upto a distance of 'n' km, then the distance travelled by the carriage in t hours is (at + n) metres and speed of the carriage is a +
n / t
km/hr
t = 20 min =
20 / 60
=
1 / 3
hrs
n = 250 m =
250 / 1000
=
1 / 4
km
Here, a = 10, t =
1 / 3
, n =
1 / 4

Using these values in the shortcut, we get:
Required speed = 10 +
1/4 / 1/3

= 10 +
3 / 4
=
40 + 3 / 4
=
43 / 4
= 10
3 / 4

Hence, the speed is 10
3 / 4
km/hr.

46. A man takes 6 hours to walk to a certain place and ride back. However, he could have gained 1 hour, if he had covered both ways by riding. How long would he have taken to walk both ways?
  A.  7 hours
  B.  4 hours
  C.  6 hours
  D.  3 hours
     
   
View Answer

Shortcut:
A man takes 't' hours to walk to a certain place and ride back. However, he could have gained 't1' hours, if he had covered both ways by riding, then the time taken by him to walk both ways is (t + t1) hours. or Both ways walking = one way walking and one way riding time + gain in time.
Here, t = 6, t1 = 1
Using these values in the shortcut, we get:
Required time = 6 + 1 = 7
Hence, he would take 7 hours.

47. A man takes 4 hours 30 minutes in walking to a certain place and riding back. He would have gained 1 hours 20 minutes by riding both ways. How long would he take to walk both ways?
  A.  6 hours 10 minutes
  B.  4 hours 30 minutes
  C.  5 hours 30 minutes
  D.  5 hours 48 minutes
     
   
View Answer

Shortcut:
A man takes 't' hours to walk to a certain place and ride back. However, he could have gained 't1' hours, if he had covered both ways by riding, then the time taken by him to walk both ways is (t + t1) hours. or Both ways walking = one way walking and one way riding time + gain in time.
t = 4 hour 30 minutes =
9 / 2
hours
t1 = 1 hour 20 min = 60 + 20 = 80 =
80 / 60
=
4 / 3
hour
Here, t =
9 / 2
, t1 =
4 / 3

Using these values in the shortcut, we get:
Required time =
9 / 2
+
4 / 3
=
(27 + 8) / 6
=
35 / 6
= 5.8
Hence, he would take 5 hours 48 minutes.

48. A man takes 3 hours 35 minutes in walking to a cerain place and riding back. He would have gained 1 hour 28 minutes by riding both ways. How long would he take to walk both ways?
  A.  3 hours 25 minutes
  B.  4 hours 3 minutes
  C.  5 hours 3 minutes
  D.  4 hours 12 minutes
     
   
View Answer

Shortcut:
A man takes 't' hours to walk to a certain place and ride back. However, he could have gained 't1' hours, if he had covered both ways by riding, then the time taken by him to walk both ways is (t + t1) hours. or
Both ways walking = one way walking and one way riding time + gain in time.
t = 3 hour 35 minutes = 180 + 35 = 215 minutes =
43 / 12
hours
t1 = 1 hour 28 min = 60 + 28 = 88 =
22 / 15
hour
Here, t =
9 / 2
, t1 =
4 / 3

Using these values in the shortcut, we get:
Required time =
43 / 12
+
22 / 15
=
215 + 88 / 60
=
303 / 60
= 5.05
Hence, he would take 5 hours 3 minutes.

49. A man takes 6 hours in walking to a certain place and riding back. He would hve gained 2 hours by riding both ways. How long would he take to walk both ways?
  A.  6 hours
  B.  8 hours
  C.  5 hours
  D.  2 hours
     
   
View Answer

Shortcut:
A man takes 't' hours to walk to a certain place and ride back. However, he could have gained 't1' hours, if he had covered both ways by riding, then the time taken by him to walk both ways is (t + t1) hours. or
Both ways walking = one way walking and one way riding time + gain in time.
Here, t = 6, t1 = 2
Using these values in the shortcut, we get:
Required time = 6 + 2 = 8
Hence, he would take 8 hours.

50. A man takes 7 hours 17 minutes in walking to a certain place and riding back. He would have gained 3 hours 17 minutes by riding both ways. How long would he take to walk both ways?
  A.  10 hour 34 minutes
  B.  09 hour 15 minutes
  C.  11 hour 30 minutes
  D.  10 hour 40 minutes
     
   
View Answer

Shortcut:
A man takes 't' hours to walk to a certain place and ride back. However, he could have gained 't1' hours, if he had covered both ways by riding, then the time taken by him to walk both ways is (t + t1) hours. or Both ways walking = one way walking and one way riding time + gain in time.
t = 7 hours 17 minutes = 420 + 17 = 437 minutes =
437 / 60
hours
t1 = 3 hours 17 minutes = 180 + 17 = 197 minutes =
197 / 60
hours
Here, t =
437 / 60
, t1 =
197 / 60

Using these values in the shortcut, we get:
Required time =
437 / 60
+
197 / 60
=
634 / 60
=
317 / 30
= 10.56
Hence, he would take 10 hours 34 minutes.

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