Model 3 Problems on average speed Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on time & distance topic of quantitative aptitude

Questions : Durga walks 5 km from her home to school in 60 minutes, then bicycles back to home along the same route at 15 km per hour. Her sister Smriti makes the same round trip, but does so at half of Durga's average speed. How much time does Smriti spend on her round trip ?

(a) 160 minutes

(b) 80 minutes

(c) 120 minutes

(d) 40 minutes

The correct answers to the above question in:

Answer: (a)

Durga's average speed

= $({2xy}/{x + y})$ kmph.

= $({2 × 5 × 15}/{5 + 15})$ kmph.

= $({2 × 5 × 15}/20)$ kmph = $15/2$ kmph

Distance of School = 5 km.

Smriti's speed = $15/4$ kmph

∴ Required time = $2(5/{15/4})$ hours

= $({2 × 5 × 4}/15) = 8/3$ hours

= $(8/3 × 60)$ minutes = 160 minutes

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Read more problems on average speed Based Quantitative Aptitude Questions and Answers

Question : 1

A person travels 600 km by train at 80km/hr, 800 km by ship at 40 km/hr 500 km by aeroplane at 400 km/hr and 100 km by car at 50km/hr. What is the average speed for the entire distance ?

a) 60$5/123$ km/hr

b) 62 km/hr

c) 65$5/123$ km/hr

d) 60 km/hr

Answer: (c)

Using Rule 3,

Total time

= $600/80 + 800/40 + 500/400 + 100/50$

= $246/8$ hours.

Average speed

= ${600 + 800 + 500 +100}/{246/8}$

= ${2000 × 8}/246 = 65{5}/123$ km/hr.

Question : 2

To cover a distance of 216 km in 3.2 hours, what should be the average speed of the car in metre/second?

a) 37.5 metre/second

b) 18.75 metre/second

c) 67.5 metre/second

d) 33.75 metre/second

Answer: (b)

Required speed of car

= $\text"Distance"/ \text"Time"$

= $(216/{3.2})$ kmph.

= $(216/{3.2} × 5/18)$ m./sec.

= 18.75 m./sec.

Question : 3

A train runs from Howrah to Bandel at an average speed of 20 km/ hr and returns at an average speed of 30 km/hr. The average speed (in km/hr) of the train in the whole journey is

a) 24

b) 25

c) 20

d) 22.5

Answer: (a)

Using Rule 5,

Average speed = ${2xy}/{x + y}$ kmph

= ${2 × 20 × 30}/{20 + 30}$

= ${2 × 20 × 30}/50$ = 24 kmph

Question : 4

A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/ hr. His average speed for the whole journey in km/hr is

a) 35

b) 40

c) 37.5

d) 37

Answer: (c)

Using Rule 5,

Average speed of whole journey

= $({2xy}/{x + y})$ kmph

= ${2 × 50 × 30}/{50 + 30}$

= ${2 × 50 × 30}/80$ = 37.5 kmph

Question : 5

A train runs at an average speed of 75 km/hr. If the distance to be covered is 1050 kms, how long will the train take to cover it ?

a) 15 hrs

b) 14 hrs

c) 13 hrs

d) 12 hrs

Answer: (b)

Using Rule 1,
Distance = Speed × Time
Speed = $\text"Distance"/\text"Time"$ , Time = $\text"Distance"/\text"Speed"$
1 m/s = $18/5$ km/h, 1 km/h = $5/18$ m/s

Time = $\text"Distance"/\text"Speed"$

= $1050/75$ = 14 hours

Question : 6

At an average of 80 km/hr Shatabdi Express reaches Ranchi from Kolkata in 7 hrs. The distance between Kolkata and Ranchi is

a) 560 m.

b) 650 m.

c) 560 km.

d) 506 km.

Answer: (c)

Distance = Speed × Time

= (80 × 7) km. = 560 km.

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