Speed, Distance & Time — Multiple Choice Questions

A speed of 90 m per min. in km per hour is:

1. 4.5

2. 5.4

3. 6

4. 6.4

Answer

60 min = 1 hour

⇒ $1 \text{ min } = \dfrac{1}{60} \text{ h }$

1000 m = 1 km

$\Rightarrow 90 \text{ m } = \Big(\dfrac{1}{1000} \times 90\Big) \text{ km } = 0.09 \text{ km }\\[1em] \text{Speed} = \dfrac{0.09 \text{ km}}{\dfrac{1}{60} \text{ h}}\\[1em] = 0.09 \times 60 \text{ km/h }\\[1em] = 5.4 \text{ km/h }$

Hence, option 2 is the correct option.

A distance of 100 km is covered at the speed of 20 km per hour and another 100 km at the speed of 30 km per hour. The average speed in this case is:

1. 25 km/h

2. 22 km/h

3. 20 km/h

4. none of these

Answer

Time taken for the first 100 km = $\dfrac{100}{20} = 5 \text{ h }$

Time taken for the next 100 km = $\dfrac{100}{30} = \dfrac{10}{3} \text{ h }$

Total distance = 100 km + 100 km = 200 km

$\text{Total time} = 5 + \dfrac{10}{3}\\[1em] = \dfrac{15 + 10}{3}\\[1em] = \dfrac{25}{3} \text{ h }\\[1em] \text{Average speed} = \dfrac{200}{\dfrac{25}{3}}\\[1em] = 200 \times \dfrac{3}{25}\\[1em] = 24 \text{ km/h }$

As 24 km/h is not among the options given,

Hence, option 4 is the correct option.

A distance of 100 m is covered in 24 seconds. The speed in km per hour is:

1. 30

2. 20

3. 15

4. 12

Answer

Solving,

$\text{Distance} = 100 \text{ m } = \dfrac{100}{1000} \text{ km } = 0.1 \text{ km }\\[1em]\text{Time} = 24 \text{ s } = \dfrac{24}{3600} \text{ h } = \dfrac{1}{150} \text{ h }\\[1em] \text{Speed} = \dfrac{0.1 \text{ km}}{\dfrac{1}{150} \text{ h}}\\[1em] = 0.1 \times 150 \text{ km/h }\\[1em] = 15 \text{ km/h }$

Hence, option 3 is the correct option.

A distance of 200 m is covered in 20 min and then 400 m is covered in 30 min; the average speed on the whole is:

1. 10 m/min

2. 12 m/min

3. 15 m/min

4. 20 m/min

Answer

Total distance covered = 200 m + 400 m = 600 m

Total time taken = 20 min + 30 min = 50 min

Average speed = $\dfrac{600 \text{ m}}{50 \text{ min}} = 12 \text{ m/min }$

Hence, option 2 is the correct option.

A distance of 300 m is covered with a speed of 20 m/min and another 300 m is covered with a speed of 25 m/min; the total time taken is:

1. 25 min

2. $13\dfrac{1}{3}$ min

3. 20 min

4. 27 min

Answer

Time taken for the first 300 m = $\dfrac{300}{20} = 15 \text{ min }$

Time taken for the next 300 m = $\dfrac{300}{25} = 12 \text{ min }$

Total time taken = 15 min + 12 min = 27 min

Hence, option 4 is the correct option.

A boy covers 300 km at a speed of 20 km/h and another 300 km at a speed of 30 km/h. The average speed on the whole is:

1. 25 km/h

2. 20 km/h

3. 24 km/h

4. 30 km/h

Answer

Time taken for the first 300 km = $\dfrac{300}{20} = 15 \text{ h }$

Time taken for the next 300 km = $\dfrac{300}{30} = 10 \text{ h }$

Total distance = 300 km + 300 km = 600 km

Total time = 15 h + 10 h = 25 h

Average speed = $\dfrac{600 \text{ km}}{25 \text{ h}} = 24 \text{ km/h }$

Hence, option 3 is the correct option.

Manish and Ravi, starting from the same place, move in opposite directions with speeds 18 m/s and 22 m/s respectively. The distance between them, in 10 seconds, will be:

1. 50 m

2. 100 m

3. 200 m

4. 400 m

Answer

As they move in opposite directions,

Relative speed = 18 m/s + 22 m/s = 40 m/s

Distance between them in 10 s = 40 × 10 m = 400 m

Hence, option 4 is the correct option.

A and B, starting from the same place move in same direction with speeds 25 m/s and 35 m/s respectively. The distance between them, in 20 seconds, will be:

1. 200 m

2. 500 m

3. 350 m

4. 1200 m

Answer

As they move in the same direction,

Relative speed = 35 m/s − 25 m/s = 10 m/s

Distance between them in 20 s = 10 × 20 m = 200 m

Hence, option 1 is the correct option.

At two instances, the speeds of a car are 40 km/h and 50 km/h, the corresponding average speed is:

1. 90 km/h

2. 5 km/h

3. 45 km/h

4. none of these

Answer

Average speed = $\dfrac{\text{Total distance covered}}{\text{Total time taken}}$

The average speed cannot be found by taking the average of the two speeds, as neither the distances covered nor the times taken at these speeds are given.

Hence, option 4 is the correct option.

A certain distance is covered in 45 minutes at 20 m/s. If the same distance is covered in 30 minutes with x m/s, then the value of x is:

1. 15

2. 20

3. 30

4. 40

Answer

Time = 45 min = 45 × 60 s = 2700 s

Distance = Speed × Time = 20 × 2700 m = 54000 m

New time = 30 min = 30 × 60 s = 1800 s

x = $\dfrac{54000 \text{ m}}{1800 \text{ s}} = 30 \text{ m/s }$

Hence, option 3 is the correct option.

A distance of 500 m is to be covered in 40 seconds, if first 200 m are covered in 20 seconds, the average speed for the remaining distance will be:

1. $8\dfrac{1}{3}$ m/s

2. 25 m/s

3. 15 m/s

4. 20 m/s

Answer

Remaining distance = 500 m − 200 m = 300 m

Remaining time = 40 s − 20 s = 20 s

Average speed for the remaining distance = $\dfrac{300 \text{ m}}{20 \text{ s}} = 15 \text{ m/s }$

Hence, option 3 is the correct option.

A certain distance is to be covered in 4 hours at the speed of 50 km/h. If the speed is reduced by 10 km/h, the time taken to cover the same distance will be increased by:

1. 9 hours

2. 5 hours

3. 2 hours

4. 1 hour

Answer

Distance = Speed × Time = 50 × 4 km = 200 km

Reduced speed = 50 km/h − 10 km/h = 40 km/h

New time = $\dfrac{200 \text{ km}}{40 \text{ km/h}} = 5 \text{ h }$

Increase in time = 5 h − 4 h = 1 h

Hence, option 4 is the correct option.

A car moves a distance of 200 km in 2 hours and 680 km in 3 hours. The average speed of car is:

1. 880 km/h

2. 176 km/h

3. 352 km/h

4. 480 km/h

Answer

Total distance covered = 200 km + 680 km = 880 km

Total time taken = 2 h + 3 h = 5 h

Average speed = $\dfrac{880 \text{ km}}{5 \text{ h}} = 176 \text{ km/h }$

Hence, option 2 is the correct option.

Two cars start from the same place in opposite directions with speeds 40 km/hr and 50 km/hr. The distance between the two cars in 3 hours is:

1. 30 km

2. 120 km

3. 150 km

4. 270 km

Answer

As the cars move in opposite directions,

Relative speed = 40 km/h + 50 km/h = 90 km/h

Distance between them in 3 h = 90 × 3 km = 270 km

Hence, option 4 is the correct option.

Two cars start from the same place in the same direction with speeds 40 km/hr and 50 km/h. The distance between the two in 3 hours is:

1. 30 km

2. 120 km

3. 150 km

4. 270 km

Answer

As the cars move in the same direction,

Relative speed = 50 km/h − 40 km/h = 10 km/h

Distance between them in 3 h = 10 × 3 km = 30 km

Hence, option 1 is the correct option.