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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

Answer:   C) 3576 sec

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 son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river  in miles/hours ?

 A) 4 mile/hr B) 6 mile/hr C) 2 mile/hr D) 5 mile/hr

Answer & Explanation Answer: B) 6 mile/hr

Explanation:

Let the speed of river and boat be 'r' m/min and 'b' m/min.
so relative speed in upstream (b-r)m/min and in downstream (b+r)m/min.
Now in upstream distnce covered in 5 min is 5(b-r)miles
so total distnce covered => 1 + 5(b-r)miles in upstream
In downstream distance covered in 5min is 5(b+r)miles
Now 1 + 5(b-r) = 5(b+r)
1+5b-5r = 5b+5r
1 = 10r
r = 1/10 mile/min => 6 mile/hr.

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1 24
Q:

Ali and Faizer are 27m apart. They both start walking and meet 9 hrs later, if they travel in the same direction and meet after 3 hrs if they walk in opposite dirction, Ali’s speed must most likely be ?

 A) 9 m/h B) 3 m/h C) 6 m/h D) 12 m/h

Answer & Explanation Answer: C) 6 m/h

Explanation:

let, speed of Ali=X mph and Faizer=Y mph

Now, relative speed when Ali is walking int the same direction with Faizer= (X-Y)mph
hence, according to question, 27/(X-Y)=9 ; solving X-Y=3; --- (1)

Now relative speed when walking in the opposite direction= (X+Y) mph
hence, according to question, 27/(X+y)=3; solving X+Y=9; --- (2)

solving 1 and 2 we get X=6 and Y=3, where X is the speed of Ali.

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1 22
Q:

A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?

 A) 9 and 3 kmph B) 6 and 7 kmph C) 8 and 1 kmph D) 7 and 2 kmph

Answer & Explanation Answer: C) 8 and 1 kmph

Explanation:

Downstream speed = 72km/8hrs  = 9 kmph
upstream speed = 84km/12hrs = 7 kmph
speed of boat = avg of downstream and upstream speeds
speed of boat = (9+7)/2kmph = 8 kmph.
current speed = half of the difference of downstream and upstream speeds
currend speed = (9-7)/2kmph = 1 kmph

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1 32
Q:

Two trains start from same place at same time at right angles to each other. Their speeds are 36km/hr and 48km/hr respectively. After 30 seconds the distance between them will be ?

 A) 900 mts B) 300 mts C) 250 mts D) 500 mts

Answer & Explanation Answer: D) 500 mts

Explanation:

Using pythagarous theorem,
distance travelled by first train = 36x5/18x30 = 300m
distance travelled by second train = 48x5/18x30 = 400m
so distance between them =√( 90000 + 160000) = √250000 = 500mts.

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4 135
Q:

An employee may claim Rs. 7.00 for each km when he travels by taxi and Rs. 6.00 for each km if he drives his own car. If in one week he claimed Rs. 595 for traveling 90 km. How many kms did he travel by taxi ?

 A) 55 kms B) 35 kms C) 25 kms D) 65 kms

Answer & Explanation Answer: A) 55 kms

Explanation:

Let x and y be the respective km's travelled by man via taxi and by his own car.
Given x + y = 90 => x = 90 - y
But according to the question,
7x + 6y = 595
7(90-y) + 6y = 595
=> 630 - 7y + 6y = 595
=> y = 630 - 595 = 35
=> x = 90 - 35 = 55
Therefore, the distance travelled by taxi is 55 kms.

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4 117