14
Q:

# A train with 120 wagons crosses Arun who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts overtaking the Arun ( he is riding on the horse) before it starts overtaking the Sriram( who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time (in seconds) after the train has crossed the Sriram do the Arun meets to Sriram?

 A) 3560 sec B) 3600 sec C) 3576 sec D) can't be determined

Explanation:

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then

$\inline \fn_jvn \frac{L}{R-A}=36$   ---------- (i)

and $\inline \fn_jvn \frac{L}{(R+K)}=24$ ---------(ii)

From eq.(i) and (ii)

3(R - A ) = 2 (R + K)

$\inline \fn_jvn \Rightarrow$    R = 3A + 2K

In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram

= 1800 ( R - A) - 24 ( A + K)

$\inline \fn_jvn \therefore$ Time required =$\inline \fn_jvn \frac{1800(R - A)-24(A+K)}{(A+K)}$

= (3600 - 24) = 3576 s

Q:

A boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?

 A) 1.8 kmph B) 2 kmph C) 2.2 kmph D) 1.5 kmph

Explanation:

Speed of Boy is B = 4.5 kmph

Let the speed of the stream is S = x kmph

Then speed in Down Stream = 4.5 + x

speed in Up Stream = 4.5 - x

As the distance is same,

=> 4.5 + x = (4.5 - x)2

=> 4.5 + x = 9 -2x

3x = 4.5

x = 1.5 kmph

2 25
Q:

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?

 A) 4.58 kms B) 6.35 kms C) 5.76 kms D) 5.24 kms

Explanation:

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream  = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance  = 2.88 x 2 = 5.76 kms

2 27
Q:

A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?

 A) 55 kmph B) 58 kmph C) 60 kmph D) 66 kmph

Explanation:

Speed on return trip = 150% of 50 = 75 km/hr.

Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.

2 63
Q:

Running 3/4th of his usual rate, a man is 15min late. Find his usual time in hours  ?

 A) 2/3 hrs B) 3/4 hrs C) 1/3 hrs D) 1/4 hrs

Explanation:

Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time

so 1/3rd of the usual time = 15min
or usual time = 3 x 15 = 45min = 45/60 hrs = 3/4 hrs.

1 73
Q:

If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ?

 A) 40 kms B) 30 kms C) 46 kms D) 32 kms

Explanation:

Let the actual distance travelled be x km.
Then x/8=(x+20)/12
=> 12x = 8x + 160
=> 4x = 160
=> x = 40 km.