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**Excercise 2**

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

The Correct answer is :8

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

The Correct answer is :11:9

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

The Correct answer is :3h

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

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