## Quant Quiz On Speed Time & Distance Day 20 Bag

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• A man in a train he can count 31 telephone posts in one minute. If they are known to be 45 m apart. Find the speed of the train.
A) 90 km/hr
B) 70 km/hr
C) 100 km/hr
D) 81 km/hr
E) 95 km/hr

Option  D
Solution:
speed of the train = 30*45 = (1350 *60)/1000 = 81 km/hr
• If a man walks from his house to office at 6 km/hr , he is late by half an hour. However, if he walks at 8 km/hr , he is late by 10 minutes only. What is the distance of his office from his house.
A) 8 km
B) 12 km
C) 14 km
D) 18 km
E) 10 km

Option  A
Solution
:
(x/6)- (x/8) = (30-10)/60
=> x = 8 km
• A candle of 8 cm long burns at the rate of 7 cm in 7 hour and another candle of 10cm long burns at the rate of 6 cm in 3 hour. What is the time required by each candle to remain of equal lengths after burning for some hours, when they start to burn simultaneously with uniform rate of burning?
A) 5 cm
B) 3 cm
C) 1 cm
D) 2 cm
E) 4 cm

Option D
Solution:
(8 – x)=(10 – 2x)
=> x = 2 cm
• Two trains, 190 m and 170 m long are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. Find the speed of each train.
A) 55 m/sec. and  42 m/sec.
B) 63 m/sec. and 57 m/sec.
C) 60 m/sec. and 55 m/sec.
D) 42 m/sec. and 40 m/sec.
E) 44 m/sec. and 40 m/sec.

Option  B
Solution:
let the speed of the faster train be x and the speed of the slower train be y . Then, When they move in the same direction , the relative speed = (x – y)
Total distance = 190 + 170  = 360 m
Now, dist. = speed * time = 360 = (x-y)*60
=> (x – y) = 6———-(1)
When the trains move in opposite direction = (x+y)
360= (x + y)*3
=> 120 =(x + y) ———–(2)
On solving (1) and (2), we get
x = 63 m/sec. and y = 57 m/sec.
• A motorcyclist covered (2/3)rd of a total journey at his usual speed. He covered the remaining distance at (3/4)th of his usual speed. As a result, he arrived 30 minutes later than the time he would have taken at usual speed. If the total journey was 180 km. What was his usual speed?
A) 30 km/hr.
B) 20km/hr.
C) 50 km/hr.
D) 40 km/hr.
E) 60 km/hr.

Option  D
Solution:
Let the usual speed be x km/hr.
(1/3)rd of the journey = 180/3 = 60km
Therefore, 60 / (3x/4) – 60/x = (1/2)
=> x = 40 km/hr.
• A boat running at the speed of 30 km/hr  downstream covers a distance of 5 km in 10 minutes . The same boat while running upstream at the same speed covers the same distance in 12 minutes . What is the speed of the current?
A)  2.5 km/hr
B)  4 km/hr
C) 3.2 km/hr
D) 1.5 km/hr
E) 2.5 km/hr

Option  A
Solution:
x  +  y = (5 * 60)/10 = 30 ——–(1)
and  x   –   y =   (5 * 60)/12  = 25 ———(2)From (1) and (2) , we get
x + y – x + y = 30 – 25 = 5
=> y = 2.5 km/hr.
• Two points P and Q are separated from a distance of 200 km. A car leaves from  P to Q at the same time another car leaves from Q to P. The two car meet at the end of 8 hours. If the car travelling from P to Q travels 20km/hr. than the other. Find the speed of the faster car?
A) 15.25
B) 20.22
C) 22.5
D) 18.9
E) 21.5

Option  C
Solution:
Let the speed of the car be x km/hr and (x+20) km/hr.
8x + 8(x+20) = 200
x = 2.5
speed of the faster carr =22.5 km/hr.
• A person takes 10 hours in walking to a place and riding back. He  would have taken 5 hours less by riding both ways.What would be the time he would take to walk both ways?
A) 5 hours
B) 15 hours
C) 12 hours
D) 10 hours
E) 8 hours

Option  B
Solution:
Time taken in walking one way and riding other way = 10 hours
Time taken in riding both the ways = 5 hours
Time taken in walking one way * 2 = 20 hours – 5 hours = 15 hours
• A man ride a bike at a speed of 6 km/hr from point X to point Y and came back from point Y to point X at the speed of 8 km/hr.  What is the ratio between the time taken by man in riding from X to Y to point Y to X respectively?
A) 3 : 5
B) 4 : 3
C) 1 : 5
D) 2 : 3
E) 2 : 7

Option   B
Solution:
Required ratio = 8 : 6 =  4 : 3
• Ritesh drive a car at the speed of  60 km/hr from  resort A to resort B. Returning over the same route , he got stuck in traffic and took an hour longer, also he could drive only at the speed of 40 km/hr . How many kilometers did he drive each way?
A) 122 km
B) 100 km
C) 120km
D) 100 km
E) 110 km

Option  C
Solution:
x /40 – x/60 = 1
=> 20x /2400 = 1
=> x = 120 km

• The speed of a boat in still water is 8kmph and the speed of current is 5kmph . The boat starts from point P and rows to point Q and comes back to point P. It takes 16 hours during this journey .Find the distance between the P and Q .
A) 42km
B) 28km
C) 31km
D) 39km
E) 47km

Option D
Solution:
Between point P and Q = x/(8-5)  + x/(8+5) = 16
=> x = 39km
• To reach from point A to point B at 4pm , Anuja will have to travel at an average speed of 18kmph . She will reach the point B at 3pm if she travels at an average speed of 24kmph . What will be the  average speed of Anuja to reach point B at 2pm ?
A) 55kmph
B) 36kmph
C) 45kmph
D) 30kmph
E) 28kmph

Option B
Solution:
From the ques. we get to know,
x/18 – x/24 = 1
=> x = 72km
Time taken at 18kmph = 72/18 = 4 hours
Therefore ,
speed to cover 72km in 2 hours  = 72/2 =  36 kmph
• Minal and Dhiraj begin together writing out a novel containing 8190 line. Minal starts with the first line , writing at the rate of 200lines per hour , and Dhiraj starts with the last line , then writes 8189th line and so on , proceeding backward at the rate of 150 lines per hour. At what line will they meet?
A) 5000
B) 4150
C) 4680
D) 5780
E) 5600

Option C
Solution:
Duration of time of their meet  = 8190/(200+150)  = 23.4 hr.
Their line of meet = 200 * 23.4 = 4680 line
• A person starts by a car from Kollam to Trivandram and at the same time another person starts from Trivandram to Kollam by a car . After passing each other  they complete their journey in 2 hours and (1/2)hour resp. At what rate does the second person drives the car if the first car runs at a speed of 40 kmph ?
A) 80kmph
B) 75kmph
C) 90kmph
D) 110kmph
E) 60kmph

Option A
Solution:
Ratio of speeds = √(1/2) : √2
=> S1 : S2 = 1 : 2
If 1 === 40
then, 2 === 80
Therefore , S2 = 80 kmph
• Suppose the telegraph poles on a railway track are 30 m apart , how many poles will be passed by a train in 2 hours if the speed of the train is 90 km an hour ?
A) 7540
B) 8750
C) 6000
D) 5240
E) 6250

Option C
Solution:
Train travels the dist. = 90 * 2 = 180 km = 180000m
Therefore,
the no. of poles = 180000/30 = 6000 poles
• The speeds of Vijaya and Keshav are 30kmph and 40kmph . Initially, Keshav is at a point A and Vijaya is at a place B . The distance between A and B is 650 km . Vijaya started her journey 3 hours earlier than Keshav to meet each other . If they meet each other at a place C somewhere in between A and B , then find the distance  between C and B.
A) 450km
B) 785km
C) 527km
D) 470km
E) 330km

Option E
Solution:
In the first 3 hours Vijaya covers 90km, so rest dist. = 560km
Now, Vijaya and Keshav travels together , towards each other.
Time = Dist./Speed = 560/70 = 8hours
Thus ,Vijaya travels total = 3 + 8 = 11 hours
Thus , the dist. traveled by Vijaya  = 11 * 30 = 330km
• A small aeroplane can travel at 400kmph in still air . The wind is blowing at a constant speed of 40kmph . The total time for a journey against the wind is 120min. What will be the time in minutes for the return journey with the wind?
A) 98.18min.
B) 220min.
C) 114min.
D) 80min.
E) 194min.

Option A
Solution:
400 – 40 = 360 kmph
Let distance be x km
Take time in hours
=> 120/60 = x/360
=> x = 720 km
Speed of aeroplane with the wind = 440 kmph
Therefore ,
Time taken by aeroplane with the wind = (720/440 ) * 60 = 98.18 min.
• There are 50 poles with a constant distance between each pole . A car takes 20 sec. to reach the 10th pole . How much more time will it take to reach the last pole ?
A) 120.11 sec.
B) 108.88 sec.
C) 88.8 sec.
D) 125.4 sec.
E) 157.17 sec.

Option C
Solution:
To reach the 10th pole, the car need to travel 9 poles
9 poles 20 seconds
1 pole (20/9) seconds
To reach the last (20th) pole, the car needs to travel 19 poles.
49 pole 49 x (20/9) seconds = 108.88 sec.
Therefore,88.8 sec more time required  to reach the last pole.
• A bike travels without stoppages at the rate of 60kmph and it travels with stoppages at the rate of 52kmph. How many minutes does the bike stop?
A) 11 mins.
B) 10 mins.
C) 5 mins.
D) 8 mins.
E) 15 mins.

Option D
Solution:
Due to stoppages, the bike can cover 8 km less per hour 60 -52 = 8
Time taken to cover 8 km =(8/60) x 60 = 8 minutes
• A cat is 50 of its own leaps behind a rat. The cat takes 5 leaps per minute to the rat’s 4 leaps. If the cat and the rat cover 8m and 5m per leap resp., what distance will the cat have to run before it catches the rat?
A) 800m
B) 1100m
C) 900m
D) 600m
E) 500m

Option A
Solution:
Speed of cat = 40m/min.
Speed of rat =20m/min.
Relative speed = 40 – 20 = 20m/min.
Diff. in dist. = 50 * 8 = 400m
Time in catching the rat  = 400/20 = 20min.
Dist. traveled in 20min. = 20 * 40 = 800m

• Two trains are running with speed 40kmph and 60kmph in the same direction. A man in the slower train passes by the faster train in 36seconds. Find the length of faster train?
A) 100mtr
B) 150mtr
C) 200mtr
D) 250mtr
E) 300mtr

Option C
Solution:

In the same direction speed … 60 -40 =2okmph
20* 5/18 * 36 =200mtr
• After travelling two hours a train met with an accident due to this it stops for an hour. After this the train moves at 66(2/3)% speed of its original speed and reaches to destination 3hour late. If the accident would occur at 200km ahead in the same line then the train reaches only 2.5hours late. Then find the distance of journey and the original speed of the train?
A) 2400km,600kmph
B) 1800km,300kmph
C) 2400km,400kmph
D) 1800km,200kmph
E) 2000km,100kmph

Option B
Solution:

Due to 200km it saves 5hrs.
For 3hrs it has to run 200*2*3 =1200km
66(2/3)% = 2/3
.                     after………..normal
speed             2         :       3
time               3         :       2
.                             3-2 =1.
1 =2 ( train stops for 1 hr out 3hrs. so 3-1 =2)
2 =4
1200/4 = 300kmph
so  2hr*300 = 600km
Now total distance = 1200 +600 = 1800km
• A man travels a distance in three equal parts. He covers first part at 20kmph,second part at 40kmph and third part at 120kmph. Find the distance if he covers total distance in 20hrs.
A) 1400km
B) 1200km
C) 1440km
D) 1600km
E) 1500km

Option C
Solution:

Distance = average speed * time
Average speed will be….72kmph
72*20 =1440km
• A person who can walk down a hill at the rate of 6kmph and climb up the hill at rate of 4kmph. He ascends and comes down to his starting point in 5hrs. how far did he ascends ?
A) 12km
B) 14km
C) 20km
D) 24km
E) 16km

Option A
Solution:

First find average speed = 2*6*4/(6+4)
Time = 5hrs
distance = 48/10 * 5 =24
one side distance = 24/2 =12km
• A student walks from his house at a speed of 2(1/2)km per hour and reaches his school 6minutes late. The next day he increases his speed by 1kmph and reaches 6minutes before school time. How far is the school from his home?
A) 5/4km
B) 9/4km
C) 7/4km
D) 11/4km
E) 10/4km

Option C
Solution:

S1*S2/difference of speed *(( late + early)/60)
= (5/2 * 7/2)/1 * 12/60= 7/4km
• In covering a distance of 60km Abhi takes 2hrs more than Sam. If Abhi triples his speed then he would take 2hrs less than Sam. Abhi speed in kmph is ?
A) 10kmph
B) 12kmph
C) 15kmph
D) 20kmph
E) 14kmph

Option A
Solution:

.              Abhi triples his speed
.                          triple…………….normal
speed                     3……………………1
time                       1…………………..3
.                                       3 -1 =2
2=4hrs
3=6hrs
so Abhi cover60km in 6hrs
60/6 =10kmph
• Two men start together to walk a certain distance, one at 5kmph and another at 4kmph. The former arrives an hour before the latter. Find the distance?
A) 10km
B) 15km
C) 20km
D) 25km
E) 30km

Option C
Solution:

.              speed          5………….4
.              time            4…………..5
.                                      5 -4 =1
1=1
5=5hrs
distance = 4*5 = 20km
• A man covers a distance in downstream at 18kmph. If the speed of stream is 2kmph then find his speed in upstream?
A) 12kmph
B) 14kmph
C) 16kmph
D) 18kmph
E) 20kmph

Option B
Solution:

.               18 – 2 – 2= 14kmph
• The distance between a thief and apolicemen is 300m. the speed of thief is 12m/s and the speed of police is 15m/s. find the distance covered by police to catch the thief?
A) 1000m
B) 1200m
C) 1500m
D) 2000m
E) 1300m

Option C
Solution:

.               300/(15-12) =100sec
15*100 = 1500m
• Two trains of same length passes each other in 36sec. if the speed of trains are 40kmph and 20kmph respectively, then find the length of train?
A) 200 m
B) 400 m
C) 600 m
D) 300 m
E) 500 m

Option D
Solution:

2x/(40+20) * 18/5 = 36
2x= 600
x = 300m

• A man covers a distance in 10hrs and in three equal parts. The speed is 10kmph, 20kmph and 60kmph respectively. Find the distance?
A) 240km
B) 300km
C) 150km
D) 180km

Option D
Solution:

Distance = speed * time
Here we need average speed. So average speed will come 18kmph
Distance = 18*10 = 180km
• Two persons covers same distance at 42kmph and 48kmph respectively. They find that the slower one takes 30minutes more to cover the distance. Find the distance cover by them?
A) 150km
B) 168km
C) 200km
D) 224km

Option B
Solution:

Speed:
42 : 48
7 : 8
Time 8 : 7
.        (+1)
1=30
8=240minutes = 4hrs
Distance = speed * time
= 42*4
= 168km
• Two persons goes from A to B at 12kmph and 8kmph. The faster one reach B first and come back. He meets slower one at a point R. find the distance between A & R if the distance between A to B is 20km?
A) 12km
B) 24km
C) 16km
D) 18km

Option C
Solution:

it is clear that both person covers double distance .
So 2*20/(12+8) =2hrs
Slower one covers 8*2 = 16km
In that time in which father one covers 12*2 =24km
So 16km is ans
• Two trains are running on a parallel track in same direction. Train A comes from behind and overtake train B in 60seconds. One person in train A observes that he covers train B in 40seconds. If the speed of trains in the ratio of 3:1, then find the ratio of length of train A & B?
A) 1:3
B) 3:2
C) 2:3
D) 1:2

Option D
Solution:

In this question speed doesn’t matter because we know …..length = speed*time. Speed remains same in both cases so it will cancel out.
Now length of A+B =60unints
Length of B = 40 units
Length of A = 60-40 =20units
A : B
20 : 40
1 : 2
• If a person cover a distance in 5/7th of his normal speed, then he will reach his destination 20minutes late. Find the usual time taken by him on his normal speed?
A) 100min
B) 50min
C) 140min
D) 70min

Option B
Solution:

Shortcut : multiply numerator by time/difference
Difference = 7-5 =2
Time = 20
5*20/2 = 50min
• A man cover a distance in t hrs, if he met with an accident after 20km and he then run at his 3/5th of his normal speed, so he reach his destination 40minutes late. If he met with an accident at 30km then he reach only 30min late. Find his original speed?
A) 60kmph
B) 50kmph
C) 40kmph
D) 24kmph

Option C
Solution:

After moving 10km more, man saves 10minutes. For saving of 40minutes he has to cover 40km.
Now speed:   after accident            before accident
.                             3                                5
Time                      5                                3
.                                            (+2)
2=40minutes
1=20min
(Normal time) 3= 60min
So he covers 40km in 60min with normal speed = 40kmph
• A thief steal a car at 1pm and run at a speed of 80kmph. The theft discovered at 2pm and police run behind him at a speed of 100kmph. Find at what time police will catch the theif?
A) 6pm
B) 7pm
C) 8pm
D) 5pm

Option A
Solution:

The thief cover 80km in 1hr.
Time – 80/(100-80) = 4hrs.
So – 2pm+4 = 6pm
• A boat travels upstream from Q to P and downstream from P to Q in 3hrs. if the distance between P to Q is 4km and the speed of the stream is 1kmph, then what is the speed of the boat in still water?
A) 4.5kmph
B) 5.2kmph
C) 2.5kmph
D) 3kmph

Option D
Solution:

Go with options
4/(3+1) + 4/(3-1) = 3hr
Only option D satisfy
• A boat covers 12km upstream and 18km downstream in 3hrs. while it covers 36km up stream and 24km downstream in 6(1/2) hrs. find velocity of the stream?
A) 1.5kmph
B) 1kmph
C) 2kmph
D) 2.5kmph

Option C
Solution:

12/y + 18/x =3…………..(1)
36/y + 24/x = 13/2……………(2)
By solving above equation we will get
X=12kmph, y = 8kmph
Speed of stream = (12-8)/2 = 2kmph
• Two person A & B with speed of 30kmph and 40kmph comes towards each other. When they meet it is find that faster one cover 30km more than slower one, find the distance cover by train?
A) 210km
B) 240km
C) 280km
D) 300km

Option A
Solution:

Faster train cover 10km more in every hour. So for 30km the train has to run for 3hrs.
Distance = (30+40) *3
= 210km