Time & Distance (14)

1. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
1. 80 km
2. 70 km
3. 60 km
4. 50 km

Answer & Explanation

Answer:- 4

Explanation :-

Let the distance covered with speed 10km = x km
Therefore , the distance covered with speed 14km = x + 20 km
Time = Distance / Speed
(x + 20)/14 = x/10    => (x + 20)/7 = x/5
5x + 100 = 7x
x = 50

 

2. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, What is the the speed of the first train?
1. 85 km/hr
2. 87.5 km/hr
3. 90 km/hr
4. 92.5 km/hr

Answer & Explanation

Answer:- 2

Explanation :-

Speed of the second train = 400/4 = 100 km/h
Speed of the First train = (100/8)*7 = 87.5 km/h

 

3. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. What is the ratio of the speed of the train to that of the car?
1. 3 : 4
2. 2 : 3
3. 1 : 2
4. 1 : 3

Answer & Explanation

Answer:- 1

Explanation :-

Let the speed of the train = x km/h  & Speed of the car =  y km/h
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car.
120/x + 480/y = 8    =>    1/x + 4/y = 1/15
If 200 km is done by train and the rest by car, then 20 minutes more time is taken.
200/x + 400/y = (8 + 20/60)
200/x + 400/y = 25/3   =>   1/x + 2/y  = 1/24
Solving both the equations,
x = 60 and y = 80
x : y = 60:80 = 3:4

 

4. Arun is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
1. 8 kmph
2. 10 kmph
3. 12 kmph
4. 14 kmph

Answer & Explanation

Answer:- 3

Explanation :-

Let the distance covered = x km
Time = Distance/Speed
(x/10) – (x/15) = 2
(3x – 2x)/ 30 = 2
(3x – 2x) = 60
x = 60 km
Time taken to cover 60 km at 10 km/hr = 60 /10 = 6 hrs
So 2 P.M. – 6 = 8 A.M starts at 8 A.M.
He starts at 8 A.M.
He have to reach at 1 P.M. i.e, in 5 hours
So, Speed = 60/5 = 12 km/hr

 

5. A car travels at an average of 50 miles per hour for 2 1/2 hours and then travels at a speed of 70 miles per hour for 1 1/2 hours. How far did the car travel in the entire 4 hours?
1. 210 miles
2. 230 miles
3. 250 miles
4. 260 miles

Answer & Explanation

Answer:- 2

Explanation :-

1st Speed = 50 miles/hour
Time taken with speed 50 miles/hr = 2 + (1/2) hour = 5/2 hour
Distance Covered with 50miles/hr in 5/2 hrs = speed * time = 50 × (5/2) = 25 × 5 = 125 miles
2nd Speed = 70 miles/hour
Time taken with speed 70 miles/hr = 1 + 1/2 hour = 3/2 hour
Distance Covered with 70miles/hr in 3/2 hrs = 70 × (3/2) = 35 × 3 = 105 miles
Total Distance = 125 + 105 = 230 miles

 

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