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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 thief goes away with a MARUTHI car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start ?

 A) 2 hrs 10 min B) 2 hrs C) 2 hrs 5 min D) 2 hrs 30 min

Answer & Explanation Answer: B) 2 hrs

Explanation:

|-----------20--------------------|
50                           40

Difference = 20kms

Relative Speed = 50 – 40 = 10 kmph

Time = 20/10 = 2 hours.

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1 15
Q:

A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?

 A) 1.5 hrs B) 1 hrs C) 2.5 hrs D) 2 hrs

Answer & Explanation Answer: D) 2 hrs

Explanation:

Speed in downstream = 96/8 = 12 kmph

Speed of current = 4 km/hr

Speed of the boatman in still water = 12 – 4 = 8 kmph

Speed in upstream = 8 – 4 = 4 kmph

Time taken to cover 8 km upstream = 8/4 = 2 hours.

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1 21
Q:

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?

 A) 180 km B) 160 km C) 140 km D) 120 km

Answer & Explanation Answer: A) 180 km

Explanation:

Speed in downstream = (14 + 4) km/hr = 18 km/hr;

Speed in upstream = (14 – 4) km/hr = 10 km/hr.

Let the distance between A and B be x km. Then,

x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.

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1 10
Q:

A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?

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

Answer & Explanation Answer: D) 1/2 kmph

Explanation:

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.

Speed in downstream = 3 x 60/18 = 10 km/hr

Rate of current = (10-9)/2 = 1/2 km/hr.

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1 7
Q:

A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed ?

 A) 1hr B) 1 hr 20 min C) 1 hr 10 min D) 50 min

Answer & Explanation Answer: B) 1 hr 20 min

Explanation:

Let the distance and original speed be 'd' km and 'k' kmph respectively.

d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3

=> (5d - 4d)/4k = 1/3 => d = 4/3 k

Time taken to cover the distance at original speed

= d/k = 4/3 hours = 1 hour 20 minutes.

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