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 person can row 8 1/2 km an hour in still water and he finds that it takes him twice as long to row up as to row down the river. The speed of the stream ?

 A) 1.78 kmph B) 2.35 kmph C) 2.83 kmph D) 3.15 kmph

Explanation:

Given speed of the person = 8 1/2 = 17/2 kmph
Let the speed of the stream = x kmph
speed of upstream = 17/2 - x
speed of downstream = 17/2 + x
But given that,
2(17/2 - x) = 17/2 + x
=> 3x = 17/2
=> x = 2.83 kmph.

4 68
Q:

Karthik could cover a distance of 200 km in 22 days while resting for 2 hrs. per day. In how many days (approx) he will cover a distance of 250 km while resting for 2 hrs. per day and moving with 2/3rd of the previous speed ?

 A) 41.25 days B) 37.5 days C) 39.75 days D) 40 days

Explanation:

Given Karthik can cover the distance of 200 kms resting 2 hrs per day in 22 days.

Let the initial speed be '1'

Hence, Time = 22(24hrs - 2)

Noe new speed = 2/3

Let the number of days he take be 'D'

Therefore, $\inline \fn_jvn \small \frac{22(24-2)x3}{200}=\frac{D(24-2)x2}{250}$

D = 11 x 3 x 5/4 = 41.25 days. = 41 1/4 days.

7 118
Q:

A bus covers its journey at the speed of 80km/hr in 10hours. If the same distance is to be covered in 4 hours, by how much the speed of bus will have to increase ?

 A) 85 km/hr B) 95 km/hr C) 105 km/hr D) 120 km/hr

Explanation:

Initial speed = 80km/hr
Total distance = 80 x 10 = 800km
New speed = 800/4 =200km/hr
Increase in speed = 200 - 80 = 120km/hr

6 172
Q:

Joel travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Joel's travel in kmph ?

 A) 38 kmph B) 40 kmph C) 60 kmph D) 54 kmph

Explanation:

Average speed = Total distance / Total time.

Total distance traveled by Joel = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 x 60 = 180 miles
Distance covered in the next 5 hours = 5 x 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8 = 37.5 mph.

we know that 1 mile = 1.6 kms

=> 37.5 miles = 37.5 x 1.6 = 60 kms

Average speed in Kmph = 60 kmph.

2 158
Q:

Two persons start running simultaneously around a circular track of length 600 m from the same point at speeds of 25 kmph and 35 kmph. When will they meet for the first time any where on the track  ?

 A) 54 sec B) 36 sec C) 72 sec D) 11 sec

Explanation:

Time taken to meet the first time = length of track/relative speed

Given the length of the track is 600 m

The relative speed = 25 + 35 = 60 kmph = 60 x 5/18 m

Therefore Time = $\inline \fn_jvn \frac{600}{(25+35)\frac{5}{18}}$  = 600/60 x (18/5) = 36 sec.