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**Excercise 1**

1. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

- 14 km
- 15 km
- 16 km
- 17 km

The Correct answer is :16 km

Let the distance travelled on foot be x km.

Then, distance travelled on bicycle = (61-x) km

So ${ \frac{x}{4}}$ + ${\frac{61- x}{9}}$ = 9

9x + 4(61-x) = 9 x 36

5x = 80

x = 16 Km

2. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. 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 P.M.?

- 8 kmph
- 11 kmph
- 12 kmph
- 14 kmph

The Correct answer is :12 kmph

Let the distance travelled by x km.

then ${\frac{x}{10}-\frac{x}{15}}$ = 2

3x-2x = 60

x = 60 km

Time taken to travel 60 km at 10 km/hr =${\frac{60}{10}}$ = 6hrs

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed = ${\frac{60}{5}}$ = 12 kmph

3. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

- 5 kmph
- 6 kmph
- 6.25 kmph
- 7.5 kmph

The Correct answer is :5 kmph

Let Abhay's speed be x km/hr.

Then, ${\frac{30}{x}-\frac{30}{2x}}$ = 3

=> 6x = 30

=> x = 5 km/hr

4. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

- 70 km/hr
- 75 km/hr
- 84 km/hr
- 87.5 km/hr

The Correct answer is :87.5 km/hr

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x = ${\frac{400}{4}}$= 100

x= ${\frac{100}{8}}$=12.5

Speed of first train = (7x12.5)km/hr =87.5 km/hr

5. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

- 9
- 10
- 12
- 20

The Correct answer is :10

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km = (${\frac{9}{54}\times60}$ ) min

= 10 min

6. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

- 50 km
- 56 km
- 70 km
- 80 km

The Correct answer is :50 km

Let the actual distance travelled be x km.

Then ${\frac{x}{10} = \frac{x+20}{14}}$

14x = 10x+200

4x = 200

x = 50 km

7. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is

- 600
- 750
- 1000
- 1250

The Correct answer is :1250

Speed =${\frac{5\times5}{18}}$ m/sec =${ \frac{25}{18}}$

Distance covered in 15 minutes ${\frac{25}{18}\times15\times60}$ m =1250 m

8. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is

- 1250
- 1000
- 750
- 600

The Correct answer is :1250

Speed = (5 x 5/18) m/sec

= 25/18 m/sec

Distance covered in 15 minutes = (25/18 x 15 x 60)m

= 1250 m

9. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?

- 15 hours
- 16 hours
- 17 hours
- 18 hours

The Correct answer is :17 hours

In this type of questions we need to get the relative speed between them

The relative speed of the boys = 5.5kmph - 5kmphn= 0.5 kmph

Distance between them is 8.5 km

Time = Distance/Speed ,

Time = ${ \frac{8.5km}{0.5kmph}}$ = 17 hrs

10. A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

- 60 km/hr
- 100 km/hr
- 110 km/hr
- 120 km/hr

The Correct answer is :120 km/hr

Number of gaps between 41 poles = 40

So total distance between 41 poles = 40x50 = 2000 meter = 2 km

In 1 minute train is moving 2 km/minute.

Speed in hour = 2x60 = 120 km/hr.

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