Time and distance is a very easy topic and has limited variety of questions. I will take up questions from each variety and will solve them with shortest method possible.

Let the distance travelled on foot be X km. Then distance travelled on bicycle will be Rs. (80 - X)

X/8 + (80 - X)/16 = 7

After forming this equation, don't solve it for X. Just observe, X/8 denotes that X is a multiple of 8 (although you can't be 100% sure, but SSC generally likes whole numbers). That means answer is either 32 km or 48 km. Put X = 32 km in the equation and check if it satisfies the equation. It does!

This is a commonly asked question. Just remember -

Time taken to cross a telephone pole = Time taken by the train to cover a distance equal to its length

Speed = 54 km/hr = 54 * 5/18 m/sec = 15 m/sec

Time taken by the train to cover a distance equal to its length = 300/15 = 20 sec

If two objects A and B are moving at a given speed and we are asked "when will A overtake B" or "When will the police catch the thief", we use the concept of

When the objects are moving in opposite direction, Relative velocity = Speed of A + Speed of B

When the objects are moving in the same direction, Relative velocity = Speed of A - Speed of B

Let the length of each train be L metres.

Here, the trains are moving in the same direction, hence relative velocity = Speed of train A - Speed of Train B = 10 km/hr = 10 * 5/18 m/sec = 25/9 m/sec

We know, Distance = Speed * Time

Here, Distance = Sum of the length of both the trains, i.e., 2L

Speed = Relative velocity

Time = Time taken by the faster train to overtake the slower train

So, 2L = 36 * 25/9

L = 50 m

Let the length of the fast train be L.

Trains are running in the same direction, hence Relative Velocity = 40 - 20 = 20 km/hr = 50/9 m/sec

L = 50/9 * 5 = 250/9 metres

This question is similar to the above question. But it has a twist! The two trains are not moving at the same time. First train is starting at 7 am, while second train is starting at 8 am.

Remember! To apply the relative velocity formula in such questions, we will first have to make the trains move at the same time. How?

Let the distance between the trains be X km

The first train takes 4 hours (7 am to 11 am) to move from A to B

Hence speed of the first train = X/4

The second train takes 3.5 hours (8 am to 11:30 am) to move from B to A

Hence speed of the second train = X/3.5

From 7 am to 8 am (1 hour), only the first train is moving. Distance travelled by the first train in 1 hour = X/4 * 1 = X/4

Distance left between the two trains = X - X/4 = (3/4)X

Relative velocity of the trains = X/4 + X/3.5

= (3/4)X / (X/4 + X/3.5)

= 1.40 hours

= 1 hour 24 minutes

So the trains will cross one another at 8 am + 1 hr 24 min = 9 : 24 am

Let the trains cross each other in t hours

First train starts early, so it will travel for complete t hours. But second train starts 1 hour after the first train, so it will travel for (t - 1) hours

Distance travelled by first train in t hours + Distance travelled by second train in (t - 1) hours = X

X/4 * t + X/3.5 * (t - 1) = X

t = 2.4 hours = 2 hours 24 minutes

But this time will be added to 7 a.m.

So, Answer = 7 a.m. + 2 hours 24 minutes = 9:24 a.m.

This question is similar to the above question.

Relative Velocity of the Thief and the Owner = 50 - 40 = 10 km/hr

Distance travelled by the thief in half an hour (from 1:30 p.m. to 2 p.m.) = 0.5 * 40 = 20 km

Now the distance between the owner and the thief is 20 km.

He will catch the thief at 2 p.m. + 2 hours = 4 p.m.

Let P and Q meet in t hours

Distance travelled by P in t hours = 20t (because the speed of P is 20 km/hr)

Distance travelled by Q in t hours = 30t (because the speed of Q is 30 km/hr)

Given, 30t - 20t = 36 km

or t = 3.6 hours

So P and Q meet after 3.6 hours

Relative velocity of P and Q = 20 + 30 = 50 km/hr

Distance between the two places = Time taken by P and Q to meet * Relative velocity = 50 * 3.6 = 180 km

Let P and Q meet at point M. P has to travel X km to reach M and Q has to travel Y km.

Time taken by P to reach M = Time taken by Q to reach M

X/20 = Y/30

X/Y = 2/3

Given, Y - X = 36 km

Divide the whole equation with Y

1 - X/Y = 36/Y

1 - 2/3 = 36/Y [Put X/Y = 2/3]

Y = 108 km

Hence X = Y - 36 = 72 km

Distance between the two places = X + Y = 108 + 72 km = 180 km

Let the distance travelled on foot be X km. Then distance travelled on bicycle will be Rs. (80 - X)

X/8 + (80 - X)/16 = 7

After forming this equation, don't solve it for X. Just observe, X/8 denotes that X is a multiple of 8 (although you can't be 100% sure, but SSC generally likes whole numbers). That means answer is either 32 km or 48 km. Put X = 32 km in the equation and check if it satisfies the equation. It does!

**Answer : (A)**

This is a commonly asked question. Just remember -

Time taken to cross a telephone pole = Time taken by the train to cover a distance equal to its length

Speed = 54 km/hr = 54 * 5/18 m/sec = 15 m/sec

Time taken by the train to cover a distance equal to its length = 300/15 = 20 sec

**Answer : (A)**If two objects A and B are moving at a given speed and we are asked "when will A overtake B" or "When will the police catch the thief", we use the concept of

**Relative Velocity**. It's very simpleWhen the objects are moving in opposite direction, Relative velocity = Speed of A + Speed of B

When the objects are moving in the same direction, Relative velocity = Speed of A - Speed of B

Let the length of each train be L metres.

Here, the trains are moving in the same direction, hence relative velocity = Speed of train A - Speed of Train B = 10 km/hr = 10 * 5/18 m/sec = 25/9 m/sec

We know, Distance = Speed * Time

Here, Distance = Sum of the length of both the trains, i.e., 2L

Speed = Relative velocity

Time = Time taken by the faster train to overtake the slower train

So, 2L = 36 * 25/9

L = 50 m

**Answer : (A)****This question is similar to Q. No. 2. We just have to replace the Speed of the train, with Relative Velocity.**

Let the length of the fast train be L.

Trains are running in the same direction, hence Relative Velocity = 40 - 20 = 20 km/hr = 50/9 m/sec

L = 50/9 * 5 = 250/9 metres

**Answer : (C)**
You can solve such questions with two methods -

__Method 1 (Relative Velocity)__
Relative velocity of A and B = 6 + 4 = 10 km/hr

They have to cover a distance to 20 km.

Hence they will meet in 20/10 = 2 hours

So if they start at 7 a.m., they will meet at 9:00 a.m.

**Answer : (C)**

__Method 2 (Equate the distance)__
Let A and B after t hours

Then distance covered by A in t hours + Distance covered by B in t hours = 20

t*4 + t*6 = 20

or t = 2 hours

__Method 1 (Relative Velocity)__Remember! To apply the relative velocity formula in such questions, we will first have to make the trains move at the same time. How?

Let the distance between the trains be X km

The first train takes 4 hours (7 am to 11 am) to move from A to B

Hence speed of the first train = X/4

The second train takes 3.5 hours (8 am to 11:30 am) to move from B to A

Hence speed of the second train = X/3.5

From 7 am to 8 am (1 hour), only the first train is moving. Distance travelled by the first train in 1 hour = X/4 * 1 = X/4

Distance left between the two trains = X - X/4 = (3/4)X

Relative velocity of the trains = X/4 + X/3.5

**Time taken by the trains to cross one another = (Distance between them) / (Relative velocity)**= (3/4)X / (X/4 + X/3.5)

= 1.40 hours

= 1 hour 24 minutes

So the trains will cross one another at 8 am + 1 hr 24 min = 9 : 24 am

**Answer (D)**

__Method 2 (Equate the distance)__Let the trains cross each other in t hours

First train starts early, so it will travel for complete t hours. But second train starts 1 hour after the first train, so it will travel for (t - 1) hours

Distance travelled by first train in t hours + Distance travelled by second train in (t - 1) hours = X

X/4 * t + X/3.5 * (t - 1) = X

t = 2.4 hours = 2 hours 24 minutes

But this time will be added to 7 a.m.

So, Answer = 7 a.m. + 2 hours 24 minutes = 9:24 a.m.

This question is similar to the above question.

*Chor-Sipahi*questions are best tackled with Relative Velocity.Relative Velocity of the Thief and the Owner = 50 - 40 = 10 km/hr

Distance travelled by the thief in half an hour (from 1:30 p.m. to 2 p.m.) = 0.5 * 40 = 20 km

Now the distance between the owner and the thief is 20 km.

**So time taken to catch the thief = Distance between them / Relative velocity**= 20/10 = 2 hoursHe will catch the thief at 2 p.m. + 2 hours = 4 p.m.

**Answer : (A)**

__Method 1 (Relative velocity)__Let P and Q meet in t hours

Distance travelled by P in t hours = 20t (because the speed of P is 20 km/hr)

Distance travelled by Q in t hours = 30t (because the speed of Q is 30 km/hr)

Given, 30t - 20t = 36 km

or t = 3.6 hours

So P and Q meet after 3.6 hours

Relative velocity of P and Q = 20 + 30 = 50 km/hr

Distance between the two places = Time taken by P and Q to meet * Relative velocity = 50 * 3.6 = 180 km

**Answer : (A)**

__Method 2__Let P and Q meet at point M. P has to travel X km to reach M and Q has to travel Y km.

Time taken by P to reach M = Time taken by Q to reach M

X/20 = Y/30

X/Y = 2/3

Given, Y - X = 36 km

Divide the whole equation with Y

1 - X/Y = 36/Y

1 - 2/3 = 36/Y [Put X/Y = 2/3]

Y = 108 km

Hence X = Y - 36 = 72 km

Distance between the two places = X + Y = 108 + 72 km = 180 km

**Answer : (A)**

**If you have any doubt in this article, please drop a comment.****Keep reading :)**

**To buy the super-hit SSC Hack-Book, follow the below link-****Buy SSC Hack Book**
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ReplyDeletein my point of view you can just revise what u read in past month because cgl is about to come in next month.to get 115 marks it's better to minimize your mistake instead of learn new thing this time..and do error question ..if you even not read grammer.. so do it atleat u can get 2 right in it so according to this u will get 2 marks for right and o.75 on wrong doing overall you will get 1.25 marks in error question ..so my suggestion do it..

DeleteThis comment has been removed by the author.

Delete1)practice old q.papers and note the techniques

Delete2)remember no sectional cutoff

3)don't waste time in GK section. Either you know or Don't know

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ReplyDeleteHello sir...i.have a doubt in q.4....here, we took length of only the faster one...wht abt the length of the other...why should we ignore that length??

ReplyDeleteBecause the "faster train" is overtaking the man. The faster train has to cover the distance equal to its length to pass the man. We take the length of the train that "overtakes"

DeleteSir in q.8....y shouldn't we proceed by simply...d/50(30-20)=36...=>d=180km

ReplyDeleteDint get you....please elaborate...

Deleted/50 is the time where the both meet...so in that specific time diff of distance travelled by both is 36km...and so on

Delete*they

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Delete2.4 hours = 2 hours 24 minutes KAISE HUA SIR?

ReplyDelete2.4 hours = 2 hours + 0.4 hours

Delete0.4 hours = 0.4*60 minutes = 24 minutes

Hence 2.4 hours = 2 hours 24 minutes

In Q.6) the expression 3/4X is a bit misleading can you make it (3/4)X or 3X/4.

ReplyDeleteThanks

in Q.8) using relative velocity concept and ratio proportion concept, it takes 2 seconds

ReplyDelete10 --> 36

50 --> ?

i.e. if 10km/hr extra gives you a lead of 36, then 50km/hr(relative velocity) will give how much? I am not sure though if this is legit :P :D

Hi prashanth sir I have dbt regarding 6th question y the adding time different for rel velocity n equate models finally when v get answer.Will u plz tell me y n for which train time v have to add the time.

ReplyDeleteHi prashanth sir I have dbt regarding 6th question y the adding time different for rel velocity n equate models finally when v get answer.Will u plz tell me y n for which train time v have to add the time.

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ReplyDeleteIf two pipes can fill a cistern of capacity 1,00,000 liters in 20 hours and 30 hours respectively, find the time taken by both of them to fill 75,000 liters of water in it.

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