tsd prepathon

7/27/2019 TSD Prepathon

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Q) Two men are walking towards each other alongside a railway track. A freight train overtakes

one of them in 20 seconds and exactly 10 minutes later meets the other man coming in the

opposite direction. The train passes this man in 18 seconds. How long after the train has passed

the second man will the two men meet? Assume constant speeds throughout. After how much

time will the two men meet each other?

5500 sec 20 5562 sec 84 4922 sec 40 6200 sec

Prepathon (Q# 1/30) Questions By MBACrackers.com

Let ‘L’ be the length of the train and ‘t’ be its speed. Let the initial distance between the two men

be ‘d’ and their speed ‘m1’ and ‘m2’. Therefore, we get L / (t - m1) = 20 and L / (t + m2) = 18 On

solving, we get t = 10m1 + 9m2 Also d / (t + m2) = 620 Therefore, d = 620 (t + m2) Substituting the

value of ‘t’, we get d = 6200 (m1 + m2) What we require is to determine the value of d / (m1 + m2)

Therefore, we get the time elapsed as 6200 secs. But this is meeting time for the initial distance d.

Hence, final answer is 6200 - 20 - 18 - 600 = 5562 secs. Hence, the correct answer is option (b).

Q) Sandeep and Naresh start simultaneously from village X to village Y, with their respective

speeds in the ratio of 3:2. After travelling one-fourth of the total distance, Naresh triples his speed

and travels for some more time, following which he again changes his speed and completes the

rest of the journey. Sandeep, however, maintains his initial speed throughout the journey. If both

Sandeep and Naresh reach the village Y at the same time, and the time for which Naresh travelled

at thrice his initial speed was one-third of his total time of travel, then find the ratio of the

respective speeds with which Sandeep and Naresh reach the village Y?

24:7 25 7:2 105 3:1 49 7:6

Let the initial speeds of Sandeep and Naresh be 3 and 2 respectively. Let the time taken by

Sandeep to reach from X to Y be t. Total time taken by Naresh to cover his journey = t Total

Distance XY = 3t Time taken by Naresh to cover the first one fourth of XY = ((3t/4))/2 = 3t/8 Time

taken by Naresh to cover the second part = t/3 Time taken by Naresh to cover the remaining part =

t-(3t/8+t/3)= 7t/24 Let the speed of Naresh for the third part of the journey be ‘v’. Now equating

the total distances covered by Sandeep and Naresh, we get 3t=3t/4+3(2)(t/3)+v(7t/24)

v(7t/24)=3t-(3t/4+2t)=t/4 v = 6/7 The ratio of their speeds = 3: 6/7 = 7: 2 Hence, the correct

answer is option (b).

A cyclist started on a road from Noida to Delhi of length 50 km at 9:00 AM. He reached Delhi with

the speed of 20 km/hr. The next day he travels back again at 9:00 AM from Noida with the speed

30 km/hr. Find the place where he will be at same point of time as day before?

30 km from Noida 80 midway 40 15 km from Noida 51 30 km from Delhi




Since time is constant in both the cases,Ratio of distances = Ratio of speeds d_1/d_2 = s_1/s_2

d_1/d_2 =2/3 Hence at 10.00 am, on his first trip he was 20 km from Noida and on return trip at

the same time, he is 30 km from Delhi. This simply means at 10.00 am he is at same place because

the total distance between Noida and Delhi is 50 km. 20 km from Noida and 30 km from Delhi.

Hence, the correct answer is option (d).


Two swimmers start from opposite end of the swimming pool. Both swimmers are swimming at

constant speeds. When they cross each other for the first time, they are 25 m from nearest side.

They reach their respective ends and on second round they meet at a distance of 20 m from the

other end. What is the length of swimming pool?

58 m waiting for answers ... 55 m waiting for answers ... 29 m waiting for answers ... 95 m

waiting for answers ...


Let the ‘length’ of swimming pool be ‘l’ meters When first has covered 25, the other swimmer has

covered (l – 25), when they meet first time. So the ratio of their speed will be proportional to the

distances covered since time taken is constant. When they meet second time, the first has covered

in all (l + 20) and second has covered (l + l – 40). Again the ratio of their speeds is proportional to

the distances covered.gh Since the ratio of speed is directly proportional to distance when time is

constant, we have 25 /l - 25 = l + 20 /2l - 20 Using compenendo and dividendo law, 25 /l = l + 20 /3l

On solving, we get l = 75 – 20 = 55 m Hence, the correct answer is option (b)


A car takes 1hr to complete a lap of a circular track at the speed of 80km/hr. If the car completes

the first lap at 40km/hr then what speed should it travel in the second lap to have an average

speed of 80km/hr for both the laps?

120 km\/hr 154 80 km\/hr 14 240 km\/hr 27 Not possible

The first lap is at 40km/hr hence the first lap takes 2hrs. For an average of 80km/hr both the laps

must be completed in 2hrs but as the first lap takes 2hrs it is not possible to get an average speedof 80km/hr. This is an impossible situation since the average can never be double of one of the

given values. Hence, the correct answer is option (d).


Parth and Antara decide to race each other from Mumbai to Pune. Antara takes the Satabdi

express train while Parth uses his Audi to travel by the Mumbai Pune Expressway. The distance

covered by both of them is the same. Antara reached Pune an hour earlier. If Parth travelled

10km/hr faster he would have reached in time with Antara but in actual time he was an hour late.



Had he travelled 20km/hr slower he would have taken 5 hours more to complete the journey.

What is the distance from Mumbai to Pune?

160 km 11 180 km 75 200 km 126 240 km 38

Let x be Parth’s normal speed be ‘x’and‘y’ be the time taken by him. Now he covers the distance Dfrom Mumbai to Pune Therefore, D = x × y Also we know, (x + 10) × (y – 1) = D or, x × y + 10y – x -

10= D But we know that x × y = D Hence, x - 10y = -10 Also from the second condition (x – 20) × (y +

5) = D or, xy -20y + 5x -100 = D or, 5x – 20y = 100 Solving the two equations we get, x = 40 km/hr

and y = 5 hours Therefore distance from Mumbai to Pune is 200km Hence, the correct answer is

option (c).


A Formula 1 car, an auto rickshaw, and a cycle racer race each other from Mumbai to Chennai. Theformula 1 car covers the 2400km distance in 8 hrs, the auto rickshaw takes 50 hrs and the cycle

racer takes 60 hrs. Find the average speed of the trio?

59 km\/hr 35 52 km\/hr 38 61 km\/hr 157 68 km\/hr 46

Average speed is defined as"TotalDistanceTravelled" /"Totaltimetaken" Since the distance is

constant, we can take the harmonic mean of the given speeds to get the value of average speed.

Average speed= 2400 × 3/(8 + 50 + 60)= 7200/118= 61.01 km/hr Hence, the correct answer is

option (c).


Ashwani travels from Baroda to Surat at the rate of 4 km/hr. Had he moved at the rate of 3.67

km/hr, he would have taken 3 hours more to reach the destination. What is the distance between

Baroda and Surat?

103 km 20 128 km 44 132 km 355 148 km

The difference between the two speeds is 0.33 km/hr.This difference would have accounted for 3

more hours of traveling.Let the total distance be “D”. Given that,3 + D/4 = D/3.67 (12 + D) × 3.67 =

4D 12 × 3.67 = 0.33 D D = 132 km Hence, the correct answer is option (c).



A group of terrorists leave Damnistan to attack Mumbai at 8:30pm and they travel with speed

20km/hr. Spiderman leaves Chicago at 9pm the same day and takes 18 hours at 200km/hr to reach

London to meet up with the global Antiterrorist Superhero Squad. The rest of the squad manages to

reach London before Spiderman. Superman is the fastest superhero but if he is alone he will be

taken out easily. He needs at least Batman and Iron man with him but they can only travel the

8000km distance between London and Mumbai at best at 150km/hr. Superman leaves, he travels at

1000km/hr, so as to reach Mumbai with Batman and Iron man, who leave instantaneously as soon

as Spiderman arrives and the terrorists reach Mumbai exactly 9 hours after Superman leaves

London. Find the distance between Damnistan and Mumbai?

2134 km 55 1098 km 58 3256 km 60 1456 km 70


Spiderman leaves Chicago at 9pm and it takes him 18 hours to reach London, so he’ll reach London

at 3pm. Batman and Iron man leave London at 3pm and reach Mumbai in 8000/150 = 53.33 hours= 2days, 5 hours and 20 mins So they’ll reach at 8:20 pm, 2 days later. Superman travels at 1000km/hr,

so he’ll reach in 8000/1000 = 8 hours. So he’ll have to leave 2 days after batman and Iron man at

12.20pm. The terrorists reach Mumbai 9 hrs after Superman leaves London i.e 9.20 pm. So the

terrorists take 3 days and 50 minutes to reach Mumbai at a speed of 20km/hr. Distance travelled =

(72 + 50/60) × 20 = 1440 + 16.67= 1456.67km Hence, the correct answer is option (d).


At the cricket World Cup, all the bowlers tried to get Sachin’s wicket by bowling 6 of their fastest

possible yorkers to him. Shoaib Akhtar’syorkers average 157 km/hr, Brett Lee averages 159 km/hr

and Shane Warne averages 158km/hr. The faster the ball, the quicker it travels to the boundary

line. The slowest and fastest ball for any bowler isn’t greater or lesser than 5km/hr of the average

of the 3 bowlers. The slowest boundary came off Brett Lee and the fastest came of Shane Warne,

find the average speed of the slowest and fastest boundary possible if the speed of the ball

travelling to the boundary is 10kms greater than the ball bowled and the slowest and fastest

deliveries are integral values?


The three bowlers bowl Yorkers at an average of 157km/hr, 158km/hr and 159km/hr. Their

average speed is 158km/hr.Since the fastest and slowest Yorker can’t be greater than or less than

5 km/hr of this average.The slowest Yorker is 153km/hr and the fastest is 163km/hr.The speed of

the boundary is 10kms additional to the speed of the ball. Therefore, the fastest boundary will be

163 + 10 = 173km/hr and the slowest boundary will be 153 + 10 = 163km/hr. The average speed of

the boundary will be (163 + 173)/2 = 168km/hr. Hence, the correct answer is option (a).




A car gives the mileage of 60km/L, 50km/L and 40km/L when driven at the speeds of 40km/hr,

50km/hr and 60km/hr respectively. Assume that each car is driven only at the three speedsmentioned above. The car is driven for 3 hours using 2 Litres of petrol. The distance covered by the

car

> 120 km 46 < 120 km 90 = 120 km 155 can not be determined 83

Let the distance traveled with 40km/hr, 50km/hr, 60km/hr is A, B and C respectively. => A/40 +

B/50+ C/60 = 3 and A/60 + B/50 + C/40 = 2. Eliminating A, we get 2B/5 + 5C/6 = 0 => B=C=0 => A =

120 km Hence, the correct answer is option (c)


Super heroes Iron-Man and Wolverine leave the same camp and run in opposite directions. Iron-

Man runs 1 mile per second (mps) and Wolverine runs 2 mps. How far apart are they in miles after

1 hour?

3400 6 10800 442 14200 8 7200

To begin, we can either convert rates to miles per hour, or we can convert the time to seconds.

Let's convert from miles per second to miles per hour. There are 3600 seconds in an hour, so if

Iron-Man runs 1 mile in a second, then he will run at 3600 ×1 = 3600 mph. Similarly, Wolverine willrun at 3600× 2 = 7200 mph. Iron man will run 3600 miles in one hour and Wolverine, whose speed

is 7200 miles per hour, will run 7200 miles in an hour. The answer is simply the sum of the distance

each runs in an hour: 3600 + 7200 = 10,800 miles apart. Hence, the correct answer is option (b).


A boat covers 40 km upstream and 90 km downstream in 5 hours. It can also cover 60 kmupstream and 60 km downstream in 5 hours. Find the speed of river?

12 km\/hr 10 3 km\/hr 8 5 km\/hr 85 10 km\/hr


Let the speed of the boat upstream be ‘U’ and speed of the boat while travelling downstream be

‘D’ 40/U+ 90/D=5 60/U+ 60/D =5 Solving the simultaneous equation, we get D = 30 km/hr and U =

20 km/hr Using the formula given in Concept cracker, we get Speed of river = "1" /"2" (D – U) =

5km/hr Hence, the correct answer is option (c).




A new car is designed for the Indian market such that its mileage at a particular speed follows a

certain relationship with that speed. Also , the speed decreases linearly with the mass of the riderwhile the petrol consumption per km increases linearly with the mass of rider .Ideally , when the

mass of the rider is negligible, the speed is 100km/hr and mileage is 100km/l .When the speed of

the Ducati is 50 km/hr , the mileage is 50 km/l.When the speed of the car is 75 km/hr , the mileage

will be

60 km\/l 12 67 km\/l 42 72 km\/l 30 75 km\/l

Speed = 100-k1*mass Petrol Consumption per KM = c2+k2*mass or Mileage = 100/(1+k2*mass)

When speed = 50KMPH, K1*mass = 50 when mileage = 50KMPL, k2*mass = 1 k1 = 50*k2 When

speed = 75kmph, k1*mass = 25 => k2*mass = 0.5 mileage = 100/1.5 = 67km/l Hence, the correct

answer is option (b).


A bus leaves from Kolkata to Delhi every hour. It takes the bus 12 hours to cover the distance. A

bus leaves Delhi for Kolkata every 2 hours. If a Person starts from Kolkata on the first bus at 6 am

and he gets off every time he sees a bus going in the opposite direction and gets on it and the

process continues in both directions. The first buses leave Delhi and Kolkata at 6 am; find out how

many bus rides he’ll take before he reaches Delhi?

48 49 24 25


When he boards the first bus he would not meet a bus in the opposite direction until halfway

through the journey. At this point P he is 6 hours into the journey.At halfway point P he’ll meet a

bus in the opposite direction, towards Kolkata. Now the next bus from Kolkata to Delhi which runs

an hour later will meet this bus half an hour into the journey. At this point Q he is through 5 and ½hours of the journey. And he’ll then board this bus to Delhi. Since the bus f rom Delhi runs at 2

hour intervals, it’ll meet the third bus at time 1 hour later than it leaves from Q. By this time the

bus for Delhi will have travelled to point R which is 6 and half hours into the journey. Thus noting

he covers just half-n-hour increment over the spot from where he took the reverse journey and in

the process takes 2 buses. The total number of buses he takes will be the 6 hour journey divided

into 12 half hour parts into the 2 buses for every increment. = 6 × 2 × 2= 24 buses Also to account

for the first bus he took to reach the halfway point, the total buses he takes is 25. Hence, the

correct answer is option (d).




Rajdhani traveling at 60 km/hr leaves Mumbai for Chandigarh at 8 am. Azad Kranti traveling at 90

km/hr also leaves Mumbai for Chandigarh at 11am. Punjab Mail leaves Chandigarh for Mumbai at11am. If all three trains meet at the same time between Mumbai and Chandigarh, what is the

speed of Punjab Mail if the distance between Chandigarh and Mumbai is 1260kms?

Let‘d’ be the distance from Mumbai where they meet, so it’s(1260 – d)kms from Chandigarh and

let‘s’ be Punjab Mail’s speed. Let Rajdhani take‘t’ hours to get to the spot, so Azad Kranti takes t -

3 and Punjab Mail takes t – 3 So we get,60t = 90(t – 3) Solving we get,t = 9 hours Distance traveled

in 9 hours = 9 × 60 = 540km Distance traveled by Punjab Mail = 1260 – 540 = 720km Time taken by

Punjab mail = 9 – 3 = 6 hrs Speed = 720/6= 120km/hr Hence, the correct answer is option (a).


A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards

the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue

vessel were to leave from the shore towards the ship and it takes 4 minutes to evacuate the crew

and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be

able to successfully rescue the people aboard the ship?


Since it takes 4 minutes to rescue the ship will travel a maximum of 16 minutes. In 20 minutes the

ship will travel = 8 × (16/60) = 2.13 km So the rescue vessel needs to travel 12 – 2.13 = 9.87km in

16 minutes = 9.87 ×(60/16) = 37.01 Km/hr Hence, the correct answer is option (d).

Whenever two of them meet, the time spent writing will be equal. Let‘t’ be that time. In time‘t’,

Ram will have painted 100 × t panels and Shyam will have painted 50 × t panels. 100 × t + 50 × t =

535 150 × t = 535 t = 535/150 = 3.56hrs In this time Ram will have painted 100 × 3.56 = 356 panels

and Shyam will have painted 50 × 3.56 = 178 panels They’ll meet on the 357th panel. Hence, the

correct answer is option (c).


Three identical trains of length 150m each are standing end to end but on 3 different tracks laid

side by side. If they travel at an average speed of 45km/hr, find out what is the least time neededto align the three trains paralleling each other?



18 seconds 24 seconds 12 seconds 15 seconds


There is a catch in this question. If we move all the 3 trains, 2 in one direction and the other in the

opposite direction the time needed for aligning will not be least as there would time wasted forthe farthest of the two trains moving in the same direction to align with each other. However if we

keep the middle train stationary and move the other two trains the time needed will be

minimized. Let us understand this with an example. Let the 3 trains be A, B and C. Consider trains

A and B to be moving in the same direction and C to be moving in the opposite direction with B

being the middle train. Now Trains B and C will align themselves in‘t’ seconds where t= ((length of

the train)/2)/(45 km/hr) t= (150/2)/(45 ×5/18)=75/12.5=6 seconds Train A will take t seconds +

time needed to cover the length of the train to align itself with the other 2 trains, as in ‘t’ seconds

it will still lag Train B by its entire length. = 6 + 150/12.5 = 6 + 12 = 18 seconds. Now let us consider

the second way of aligning where one of the trains remains stationary. Let Train B which the

middle train be stationery, and the other two trains move in opposite directions. Time taken by

trains A and c will be equal to the time taken by the trains to cover the length of Train B =

150/12.5 = 12 seconds. Therefore, the shortest time needed is 12 seconds Hence, the correct

answer is option (c).


Varun goes sailing, His boat can propel forward on its internal engine at 12km/hr. The flow of the

sea is 4km/hr south and the wind is blowing 6km/hr north. If he has to sail north to Check point A

and then return to the starting point along the same route. If he takes a 2 hours less while going to

the check point than returning, find the distance between the Check Point and the starting point?

90 km 16 60 km 44 80 km 38 70 km

While going north the Wind will assist his movement while the sea will oppose it, so we have to

add the speed of the wind and subtract the speed of the sea. On the other hand while going south

the wind will oppose the movement and the sea will assist the boat, so we have to subtract the

wind speed and add the sea speed. Let D be the distance between the starting point and check

post. So we get, D/((12-4+6))+ 2= D/((12+4-6)) D/14+ 2=D/10 4D/140=2 D = 70km. Hence, the

correct answer is option (d).

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