Speed, Time and Distance
 In a race of one kilometre, A gives B a start of 100 metres and still wins by 20 seconds. But if A gives B a start of 25 seconds, B wins by 50 metres. The time taken by A to run one kilometre is

 17 seconds

500 seconds 29 
1200 seconds 29 
700 seconds 29

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Let A take x seconds in covering 1000m and b takes y seconds
According to the question,x + 20 = 900 y 1000 ⇒ x + 20 = 9y ...(i) 10 and, 950 x + 25 = y ...(ii) 1000
From equation (i),10x + 200 = y 9 9 ⇒ 10x + 200 = 950x + 25 9 9 1000 ⇒ 10x + 200 = 19x + 25 9 9 20 ⇒ 10x − 19x = 25 − 200 9 20 9 = 200x − 171x = 225 − 200 180 9 ⇒ 29x = 25 180 9 ⇒ x = 25 × 180 = 500 seconds. 9 29 29 Correct Option: B
Let A take x seconds in covering 1000m and b takes y seconds
According to the question,x + 20 = 900 y 1000 ⇒ x + 20 = 9y ...(i) 10 and, 950 x + 25 = y ...(ii) 1000
From equation (i),10x + 200 = y 9 9 ⇒ 10x + 200 = 950x + 25 9 9 1000 ⇒ 10x + 200 = 19x + 25 9 9 20 ⇒ 10x − 19x = 25 − 200 9 20 9 = 200x − 171x = 225 − 200 180 9 ⇒ 29x = 25 180 9 ⇒ x = 25 × 180 = 500 seconds. 9 29 29
 A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in :

 18 minutes
 24 minutes
 16 minutes
 12 minutes

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Ratio of the speed of A, B and
C = 6 : 3 : 1
⇒ Ratio of the time taken= 1 : 1 : 1 = 1 : 2 : 6 6 3 ∴ Time taken by A = 72 = 12 minutes 6 Correct Option: D
Ratio of the speed of A, B and
C = 6 : 3 : 1
⇒ Ratio of the time taken= 1 : 1 : 1 = 1 : 2 : 6 6 3 ∴ Time taken by A = 72 = 12 minutes 6
 In a onekilometre race A, B and C are the three participants. A can give B a start of 50 m. and C a start of 69 m. The start, which B can allow C is

 17 m.
 20 m.
 19 m.
 18 m.

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Let the time taken to complete the race by A,B, and C be x minutes.
∴ Speed of A = 100 , x B = 1000 − 50 = 950 x x C = 1000 − 69 = 931 x x
Now, time taken to complete the race byB = 1000 = 1000 × x 950/x 950 and distance travelled by C in 1000x min 950 = 1000x × 931 = 980 km. 950 x
∴ B can allow C
= 1000 – 980 = 20 mCorrect Option: B
Let the time taken to complete the race by A,B, and C be x minutes.
∴ Speed of A = 100 , x B = 1000 − 50 = 950 x x C = 1000 − 69 = 931 x x
Now, time taken to complete the race byB = 1000 = 1000 × x 950/x 950 and distance travelled by C in 1000x min 950 = 1000x × 931 = 980 km. 950 x
∴ B can allow C
= 1000 – 980 = 20 m
 A train 110 metre long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

 5 seconds
 6 seconds
 7 seconds
 10 seconds

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Relative speed of train
= (60 + 6) kmph.= 66 × 5 m/sec. 18 = 55 m/sec. 3
Length of train = 110 metre∴ Required time = 110 seconds 55/3 = 110 × 3 seconds 55
= 6 secondsCorrect Option: B
Relative speed of train
= (60 + 6) kmph.= 66 × 5 m/sec. 18 = 55 m/sec. 3
Length of train = 110 metre∴ Required time = 110 seconds 55/3 = 110 × 3 seconds 55
= 6 seconds
 The time for a train of length 110 metre running at the speed of 72 km/hr to cross a bridge of length 132 metre is

 9.8 seconds
 12.1 seconds
 12.42 seconds
 14.3 seconds

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Speed of train = 72 kmph.
= 72 × 5 m./sec. 18
= 20 m./sec.Required time = Length of train and bridge Speed of train = 110 + 132 seconds 20 = 242 seconds 20
= 12.1 secondsCorrect Option: B
Speed of train = 72 kmph.
= 72 × 5 m./sec. 18
= 20 m./sec.Required time = Length of train and bridge Speed of train = 110 + 132 seconds 20 = 242 seconds 20
= 12.1 seconds