Quiz 5

Bus A
Travels 200km @ 40kmph
the next 200km @ 50kmph and
the final 200km @ 60kmph

So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins

Bus B
Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip.
So, Bus B will travel 160 kms in the first 4 hours , 200 kms in the next 4 hours and 240 in the final 4 hours
So, both buses cross each other when they are in their middle legs.

After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50).

The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph.

Time taken = 190100190100= 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 km from City N and 295 km from city A.

The question is When and where will the two buses cross each other?

Hence, the buses cross 295 km from city A.

Given :
car of length = 4 m
length of truck = 20 m
Speed of truck = 36 km/hr

Approach:
Total distance to be covered by the car d = 20 + 4 = 24 m
Let speed of car be S1 m/s
Speed of truck S2 = 36 km/hr = 10 m/s
Both the car and the truck are travelling in the same direction and we know that to overtake the truck, the speed of the ca should be more than that of the truck.
Hence, relative speed = |S1 - S2|
Time to overtake = 10s

S = dtdt
|S1 - 10| = 24102410
S1 - 10 = 2.4
S1 = 10 + 2.4 = 12.4 m/s

The question is  At what speed should the car travel?

Hence, the answer is 12.4 m/s

Let the length of Train A be x meters
Let speed of Train B be y kmph
Relative distance = Relative speed * time taken to cross/overtake

Crossing scenario:
Relative speed of 2 trains = 63 + y
Time taken to cross = 27 sec or 27/3600 hrs
Relative distance between 2 trains = Length of Train A + length of train B = (x + 0.5) km
Therefore, x + 0.5 = (63 + y) * 27 / 3600 ----- (1)

Overtaking scenario:
Relative speed of 2 trains = 63 – y
Time taken to overtake = 162 sec or 162/3600 hrs
Relative distance between 2 trains = x + 0.5
Therefore, x + 0.5 = (63 – y) * 162/3600 --- (2)
From (1) and (2), solve for y.
(63 + y) * 27 = (63 – y) * 162
27y + 162 y = 63*162 – 63 *27
189y = 63 * 135 or y = 45 kmph

Substitute in (2) to get x.
x + 0.5 = (63 – 45) * 162/3600
Or x = 0.31 km or 310 meters

The question is \"If the length of train B is 500 meters, find the length of Train A.\"

Hence, the answer is 310 m

Choice D is the correct answer.

Distance covered by P in 8 sec = 4 * 8 = 32 m
Distance covered by P in 16 sec = 32 + 5 * 8 = 72 m
Distance covered by P in 24 sec = 72 + 6 * 8 = 120 m
Distance covered by P in 32 sec = 120 + 7 * 8 = 176 m
Distance covered by P in 40 sec = 176 + 8 * 8 = 240 m
Distance covered by P in 48 sec = 240 + 9 * 8 = 312 m
Total distance in 48 sec = 312m
To cover balance 86 m with speed = 10 m/sec, time taken = 86/10 = 8.6 sec
So P would finish 400 m in 48 + 8.6 = 56.6 seconds.

In 56.6 seconds, Q cycles 56.6 * 6.5 = 367.9 m or B should have a 32.1 m lead to result in a dead heat.

The question is If P and Q had to cycle for a 400 m race, how much lead in terms of distance, can P give Q and still finish at the same time as Q?

Hence, the answer is 32.1 m

 speeds are related to!

Let the speed of the bus be ‘b’ and man be ‘m’.
Let the distance between P and A be y.
AC:CB = 1:3 implies AC = x and CB = 3x

When bus goes from P to A and the man from C to A, time taken by both are equal and they meet at A.
y/b = x/m or
b/m = y/x --- (1)

When bus goes from P to B and the man from C to B, again time taken by both are equal and they meet at B.
(y+x+3x)/b = 3x/m
b/m = (4x+y)/3x ---(2)

Equating (1) and (2), we get y/x = (4x+y)/3x
3y = 4x + y or y = 2x

Therefore ratio of speeds b/m = 2x/x or 2 : 1

The question is \"When the bus starts at P and if the man starts running towards A, he will meet the bus at A. But if he runs towards B, the bus will overtake him at B. Which of the following is true?\"

Hence, the Bus travels 2x times faster than the man.

Choice B is the correct answer.

Total time = 6.5 hrs
Let the total distance be x
Ramesh\'s speeds = 30, 45, 60 kmph

6.5 = x/330x/330 + x/345x/345 + x/360x/360
6.5 = 2x+4x/3+x1802x+4x/3+x180
6.5 = 6x+4x+3x5406x+4x+3x540
or x = 270 km

With each speed distance covered = 270/3 = 90 km
Fuel consumed when driving at 30 = 90/11 = 8.1 l
Fuel consumed when driving at 45 = 90/14 = 6.4 l
Fuel consumed when driving at 60 = 90/18 = 5
Total fuel = 8.1 + 6.4 + 5 = 19.5 liters

When Arun drives the car, he should drive at 60 kmph throughout so that he gets the maximum mileage!
Fuel consumption when driving at 60 for entire journey = 270/18 = 15 liters

The question is  So he decides to drive Ramesh\'s car one day from city A to city B. How much fuel will he be able to save?
Difference = 19.5 – 15 = 4.5

Hence, the answer is 4.5 liters.

Choice B is the correct answer.

When Antony completes, Amar would have run (x – 14) m; Time taken is the same
Ratio of Amar’s speed : Antony’s speed = x−14t1x−14t1 : xt1xt1 or x−14xx−14x ---- (1)

When Akbar finishes, Amar would have run (x – 32) m; Antony would have run (x – 20) m; Time taken is the same

At this point, the ratio of Amar’s speed : Antony’s speed = x−32t2x−32t2 : x−20t2x−20t2 or x−32x−20x−32x−20 ---- (2)
Equating (1) and (2), we get
x−14xx−14x = x−32x−20x−32x−20
x² – 34x + 280 = x² – 32x
2x = 280
Or x = 140 m
Ratio of Amar’s speed : Antony’s speed = (140−14)140(140−14)140 = 126140126140 = 910910

The question is What is Amar’s speed?

Hence, Amar Speed is 9/10^th of Antony Speed

Let the distance between A and B be ‘x’ miles.
Let their speeds be T, J and B in miles/hour

When Tom meets Jerry:
Distance travelled by Tom = x + 9
Distance travelled by Jerry = x – 9
Time taken will be the same => x+9Tx+9T = x−9Jx−9J
Or TJTJ = x+9x−9x+9x−9 --(1)

When Jerry meets Bill:
Distance travelled by Jerry = x + 7
Distance travelled by Bill = x – 7
Time taken will be the same => x+7Jx+7J = x−7Bx−7B
Or JBJB = x+7x−7x+7x−7 --(2)

Given 3T = 5B
or TBTB = 5353
From (1) and (2)
TBTB = TJTJ * JBJB
5(x - 9)(x - 7) = 3 (x + 9)(x + 7)
5x² – 80x + 315 = 3x² + 48x + 189
2x² – 128x + 126 = 0
x² – 64x + 63 = 0
x = 63 or x = 1

The question is \\\" What could be the distance between the points A and B?\\\"
Therefore, X has to be 63.

Hence, the answer is 63 miles.

x, y or z cannot be greater than 24
Also x + y + z cannot be greater than 24
Given x hrs + z hrs = y hrs
Also y min + x min = z min
The only value of x that will satisfy the above 2 equations is 0.
Hence, from among the choices given, the time could be 00:02 hrs

The question is  If the total travel time was z hrs and x minutes, his starting time in Chennai could have been ______

Hence, the answer is 00:02 hrs

Choice C is the correct answer.

Here, the distance travelled by Sourav is constant in both the cases.
So,20 * t = 25 * (t-1) = D
=> 20t = 25t - 25
=> 5t = 25
=> t = 5 hrs So, Distance travelled = 20 * 5 = 100 Km.

The question is \"What is the distance usually covered by him?\"

Hence, the answer is 100 km

Choice B is the correct answer.