# Time and Distance - Excercise 1

## Questions

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

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

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

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.