Practice Problems on average speed - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A man goes from A to B at a uniform speed of 12 kmph and returns with a uniform speed of 4 kmph His average speed (in kmph) for the whole journey is :
(a)
(b)
(c)
(d)
Using Rule 5,
If two equal distances are covered at two unequal speed of x kmph and y kmph,
then average speed = $({2xy}/{x + y})$
= ${2 × 12 × 4}/{12 + 4} = 96/16$ = 6 kmph
Q-2) A man goes to a place on bicycle at speed of 16 km/hr and comes back at lower speed. If the average speed is 6.4 km/hr in total journey, then the return speed (in km/hr) is :
(a)
(b)
(c)
(d)
Let the speed of cyclist while returning be x kmph.
Average speed = ${2 × 16 × x}/{16 + x}$
6.4 = ${32x}/{16 + x}$
6.4 × 16 + 6.4x = 32x
32x - 6.4x = 6.4 × 16
25.6x = 6.4 × 16
$x = {6.4 × 16}/{25.6}$ = 4 kmph.
Q-3) On a journey across Kolkata, a taxi averages 50 km per hour for 50% of the distance, 40 km per hour for 40% of it and 20 km per hour for the remaining. The average speed (in km/hour) for the whole journey is :
(a)
(b)
(c)
(d)
Using Rule 2,
Total distance = 100 km.
Total time = $50/50 + 40/40 + 10/20$
= $1 + 1 + 1/2 = 5/2$ hours
Average speed = ${100 × 2}/5$ = 40 kmph
Q-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)
(b)
(c)
(d)
Using Rule 5,
Average speed of whole journey
= $({2xy}/{x + y})$ kmph
= ${2 × 50 × 30}/{50 + 30}$
= ${2 × 50 × 30}/80$ = 37.5 kmph
Q-5) 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)
(b)
(c)
(d)
Using Rule 5,
Average speed = ${2xy}/{x + y}$ kmph
= ${2 × 20 × 30}/{20 + 30}$
= ${2 × 20 × 30}/50$ = 24 kmph
Q-6) With an average speed of 40 km/ hr, a train reaches its destination in time. If it goes with an average speed of 35 km/hr, it is late by 15 minutes. The total journey is
(a)
(b)
(c)
(d)
Let the length of journey be x km, then
$x/35 - x/40 = 15/60 = 1/4$
${8x - 7x}/280 = 1/4$
$x = 280/4 = 70$ km
Q-7) A man walks from his house at an average speed of 5 km per hour and reaches his office 6 minutes late. If he walks at an average speed of 6 km/h he reaches 2 minutes early. The distance of the office from his house is
(a)
(b)
(c)
(d)
Required distance of office from house = x km. (let)
Time = $\text"Distance"/ \text"Speed"$
According to the question,
$x/5 - x/6 = {6 + 2}/60 = 2/15$
${6x - 5x}/30 = 2/15$
$x/30 = 2/15$
$x = 2/15$ × 30 = 4 km.
Using Rule 10,If a man travels at the speed of $s_1$, he reaches his destination $t_1$ late while he reaches $t_2$ before when he travels at $s_2$ speed, then the distance between the two places is D = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
Here, $S_1 = 5, t_1 = 6, S_2 = 6, t_2$ = 2
Distance = ${(S_1 × S_2)(t_1 + t_2)}/{S_2 - S_1}$
= ${(5 × 6)(6 + 2)}/{6 - 5}$
= $30 × 8/60$ = 4 km.
Q-8) P travels for 6 hours at the rate of 5 km/ hour and for 3 hours at the rate of 6 km/ hour. The average speed of the journey in km/ hour is
(a)
(b)
(c)
(d)
Using Rule 2,If a man travels different distances $d_1,d_2,d_3$,... and so on in different time $t_1,t_2,t_3$ respectively then,Average speed= $\text"total travelled distance"/\text"total time taken in travelling distance"$= ${d_1 + d_2 + d_3 +...}/{t_1 + t_2 + t_3 +...}$
Total distance
= 5 × 6 + 3 × 6
= 30 + 18 = 48 km
Total time = 9 hours
Average speed
= $48/9 = 16/3 = 5{1}/3$ kmph
Q-9) At an average of 80 km/hr Shatabdi Express reaches Ranchi from Kolkata in 7 hrs. The distance between Kolkata and Ranchi is
(a)
(b)
(c)
(d)
Distance = Speed × Time
= (80 × 7) km. = 560 km.
Q-10) 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)
(b)
(c)
(d)
Using Rule 1,Distance = Speed × TimeSpeed = $\text"Distance"/\text"Time"$ , 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