# Time and Distance - Excercise 1

## Questions

1.   A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is

• 35.55 km/hr
• 36 km/hr
• 71.11 km/hr
• 71 km/hr
The Correct answer is :71.11 km/hr

Total time taken= ${\frac{160}{64}+\frac{160}{80}}$ hrs = ${\frac{9}{2}}$ hrs
Average speed = ${320\times\frac{2}{9}}$ =71.11 km/hr

2.   A person goes to his office at 1/3rd of the speed at which he returns from his office. If the average speed during the whole trip is 12 m /h . what is the speed of the person while he was going to his office?

• 10
• 6
• 8
• can't be determined

u = k , v = 3k
then => ${\frac{2\times k\times 3k}{k+3k}}$ = 12 => 1.5k =12 => k= 8km/h

3.   Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

• 9:20
• 11:9
• 11:20
• None of these

Total distance is 200 Km. If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9

4.   A Person X started at 3 hours earlier at 40km/h from a place P, then another person Y followed him at 60km/h. Started his journey at 3 O'clock, afternoon. What is the diference in time when X was30 km ahead of Y and when Y was 30 km ahead of X?

• 2h
• 3h
• 3.5h
• 4.25h

Time ( when X was 30 km ahead of Y) =${ \frac{120-30}{20}}$= 4.5 h
Time ( when Y was 30 km ahead of X) =${ \frac{120+30}{20}}$= 7.5 h
Thus, required difference in time = 3h

5.   Akash leaves mumbai at 6 am and reaches Bangalore at 10 am . Prakash leaves Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?

• 10 a.m
• 08:32 a.m
• 08:56 a.m
• 09:20 a.m
The Correct answer is :08:56 a.m

Time taken by Akash = 4 h
Time taken by Prakash = 3.5 h
For your convenience take the product of times taken by both as a distance.
Then  the distance = 14km
Since, Akash covers half of the distance  in 2 hours(i.e at 8 am)
Now, the rest half (i.e 7 km) will be coverd by both prakash and akash
Time taken by them = 7/7.5 = 56 min
Thus , they will cross each other at  8 : 56am.

6.   Arjun and Bhishma are running on a circular track of length 600m. Speed of Arjun is 30 m/s and that of Bhishma is 20 m/s .They start for the same point at the same time in the same direction. When will they meet again for the first time?

• 45 sec
• 15sec
• 25 sec
• 60 sec
The Correct answer is :60 sec

Time= circumference/speed = ${\frac{600}{10}}$= 60 sec
Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma,
They will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.
Since, they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.

7.   A and B runs around a circular track. A beats B by one round or 10 minutes. In this race, they had completed 4 rounds. If the race was only of one round, find the A's time over the course:

• 8 min
• 7.5 min
• 12.5 min
• 12 min
The Correct answer is :7.5 min

B runs around the track in 10 min i.e , Speed of B = 10 min per round
A beats B by 1 round
Time taken by A to complete 4 rounds
Time taken by B to complete 3 rounds = 30 min
A's speed = ${ \frac{30}{4}}$ = 7.5 min per round
Hence, if the race is only of one round then A's time over the course = 7 min 30 sec

8.   An athlete runs 200 meters in 24 seconds. His speed is ?

• 10 km/hr
• 17 k/hr
• 27 km/hr
• 30 km/hr
The Correct answer is :30 km/hr

Speed = ${\frac{Distance}{Time}}$ = ${\frac{200}{24}}$ m/sec = ${\frac{25}{3}}$ m/sec
= ${ \frac{25}{3}\times\frac{18}{5}}$ km/hr = 30 km/hr.

9.   A cyclist covers a distance of 750 meter in 2 minutes 30 seconds. What is the speed in km/hr of cyclist

• 16 km/hr
• 17 km/hr
• 18 km/hr
• 19 km/hr
The Correct answer is :18 km/hr

Speed = Distance/Time
Distance = 750 meter
Time = 2 min 30 sec = 150sec
Speed = ${\frac{750}{150}}$ = 5m/sec
${5\times\frac{18}{5}}$km/hr = 18 km/hr

10.   A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?

• 10 meters
• 25 meters
• 45 meters
• 35 metres
The Correct answer is :35 metres

A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat.
Let the speed of b be 4x then speed of a is 1.25*4x=5x
Given by the time B runs Dkms A can cover D+7 kms
so D/4x=(D+7)/5x
5xD=4xD+ 28x
or xD= 28x
or D=28
so the length of the race is 28+7=35