A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

Correct Answer: 82 km/hr

Explanation:

Let the speed of the second train be x km/hr.

Relative speed	= (x + 50) km/hr
	= [ (x + 50) x 5 ] m/sec 18
	= [ 250 + 5x ] m/sec. 18

Distance covered = (108 + 112) = 220 m.

∴	220	= 6
	❨ 250 + 5x ❩ 18

⟹ 250 + 5x = 660

⟹ x = 82 km/hr.

Correct Answer: 60 km/hr

Explanation:

Let the speed of the slower train be x m/sec.

Then, speed of the faster train = 2x m/sec.

Relative speed = (x + 2x) m/sec = 3x m/sec.

∴	(100 + 100)	= 3x
	8

⟹ 24x = 200

⟹ x =	25	.
	3

So, speed of the faster train =	50	m/sec
	3

=	❨	50	x	18	❩km/hr
		3		5

   = 60 km/hr.

Correct Answer: 24 sec

Explanation:

Relative speed =	= (45 + 30) km/hr
	= ❨ 75 x 5 ❩ m/sec 18
	= ❨ 125 ❩ m/sec. 6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

∴ Required time =	❨	500 x	6	❩	= 24 sec.
			125

Correct Answer: 50 m

Explanation:

2 kmph =	❨	2 x	5	❩	m/sec =	5	m/sec.
			18			9

4 kmph =	❨	4 x	5	❩	m/sec =	10	m/sec.
			18			9

Let the length of the train be x metres and its speed by y m/sec.

Then,	❨	x	❩	= 9 and	❨	x	❩	= 10.
		y - 5 9				y - 10 9

∴ 9y - 5 = x and 10(9y - 10) = 9x

⟹ 9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

∴ Length of the train is 50 m.

Correct Answer: 89 sec

Explanation:

Speed =	❨	240	❩m/sec = 10 m/sec.
		24

∴ Required time =	❨	240 + 650	❩sec = 89 sec.
		10

Correct Answer: Data inadequate

Explanation:

One of AB, AD and CD must have given.

So, the data is inadequate.

Correct Answer: 9.2 m

Explanation:

Let AB be the wall and BC be the ladder.

Then, ∠ACB = 60° and AC = 4.6 m.

AC	= cos 60° =	1
BC		2

⟹ BC	= 2 x AC
	= (2 x 4.6) m
	= 9.2 m.

Correct Answer: 21.6 m

Explanation:

Let AB be the observer and CD be the tower.

Draw BE ⊥ CD.

Then, CE = AB = 1.6 m,

      BE = AC = 20√3 m.

DE	= tan 30° =	1
BE		√3

⟹ DE =	20√3	m = 20 m.
	√3

∴ CD = CE + DE = (1.6 + 20) m = 21.6 m.

Correct Answer: 173 m

Explanation:

Let AB be the tower.

Then, ∠APB = 30° and AB = 100 m.

AB	= tan 30° =	1
AP		√3

⟹ AP	= (AB x √3) m
	= 100√3 m
	= (100 x 1.73) m
	= 173 m.

Correct Answer: 30°

Explanation:

Let AB be the tree and AC be its shadow.

Let ∠ACB = Θ.

Then,	AC	=	√3     ⟹     cot Θ = √3
	AB

∴ Θ = 30°.