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Direction : Read the following questions carefully and choose the right answer.
1
A man can reach a certain place in 40 hours. If he reduces his speed by 1/15th, he goes 5 km less in that time. Find the total distance covered by him.
» Explain it
C
Let Distance = D km, Speed = S km/h

Time =  Distance
Speed

40 =  Distance  .... (1)
Speed

After reducing speed,
Distance = Distance – 5 km, Speed = S ×  14  km/h
15

Time =  Distance
Speed

40 =  (Distance – 5)  ....  (2)
Speed × 14
  15

After solving equation 1 and 2
 
Distance  =  (Distance – 5)
Speed Speed × 14
    15

14 Distance = 15 (Distance – 5)

14 Distance = 15 Distance – 75

Distance = 75 km.

Hence, option C is correct.
 
2
A person travelled 132 km by auto, 852 km by train and 248 km by bike. It took 21 hours in all. If the speed of train is 6 times the speed of auto and 1.5 times speed of bike, what is the speed of train?
» Explain it
C
Let the speed of auto be x kmph-1 . So, the speed of train will be 6x and that of bike will be

=      6 x  = 4x
1.5

As per the given information,

Time taken by auto + Time taken by train + Time taken by bike = 21 hours
 
⇒   132  +  852  +  248  = 21
x 6x 4x

or,  132  +  142  +  62  = 21
x x x

or,  21x = 132 + 142 + 62 = 336
 
∴   x =  336  = 16
21

∴   Speed of the train = 6x =  6 × 16 = 96 kmh-1

Hence, option C is correct.
 
3
A car drove from Agra to Delhi without stopping. It covered the first 50 miles of its journey at an average speed of 25 mph. What was the car’s average speed (in mph), for the remaining 130 miles if its overall average speed was 45 mph?
» Explain it
D
Average speed =  total distance  
total time

Total distance = 50 + 130 = 180 miles
 
  Total time =  180  = 4 hours.
45

Time spent for the first 50 miles =  50  = 2 hours
25

∴  Time spent on the remaining journey = 4 − 2 = 2 hours
 
∴  Average speed for the remaining 130 miles =  130  = 65 mph
2

Hence, option D is correct.
 
4
A motor car does a journey in 16 hours, covering the first half at 30 Km/hr and the second half at 50 Km/hr. What is the distance covered?
» Explain it
E
Since different speeds are traveled for equal distance, the average speed can be found out

Average speed =  (2 × 30 × 50)  =  300  km/h
(30 + 50) 8

Distance covered =  300  × 16 = 600 km  
8

Hence, option E is correct.

5
A and B are two stations 1200 km apart. Train X starts from station A towards station B at 60 kmph 2 hours before train Y starts from station B towards station A. If they meet at a point 360 km from station B, What is the speed of Train Y?
» Explain it
D
The distance covered by X in 2 hours is 2 × 60 = 120 km

The distance remaining is 1080 km

This distance travelled before meeting is directly proportional to their speed

They meet 360 km from B. Hence, train Y must've travelled 360 km

X has travelled 720 km and Y has travelled only 360 km in the same time

This means that speed of X is twice of Y

Since speed of X is 60 kmph therefore speed of Y is 30 kmph

Hence, option D is correct.