Problems on Trains Aptitude Questions and Answers

Hi, Welcome back to learn aptitude. Today we are going to look take a look on Problems on Trains. As you can see in any aptitude examination, you can find at least one Train based problem. In this post you will get various basic Problems on Trains. So lts get started.

Problems on Train Formulas

1. Unit Conversion Formula

Conversion is a simple problem that you may face in the every Train based problems. The conversion problems are to convert Km/Hour to Meter/Sec or Meter/Sec to Km/Hour.

So when the question is to convert KM/Hour to Meter/Second then we have to multiply by 518 , and when the question asking to convert meter/sec to Km/Hour then multiply by 185 .

  • ‘A’ Km/Hour = A × 518  M/Sec
  • ‘B’ m/Sec = B ×  .18 Km/Hour

Q.1 Convert 54 Km/Hr to M/Sec?

Solution: 54Km/Hour= 54 × 518  =15 m/Sec

Q.2 Convert 50 m/Sec to Km/Hr?

Solution: 50 m/Sec= 50 × 18 =180 Km/Hr

2. Time and Distance Formula

The most important formula to solve Problems on Trains is Time and Distance formula. So just Remember this formula and your rest work is done.

Let Distance covered by the train =d

and the time take by the train = t

Hence Speed of the Train ‘s’= Distance/time 

Q. A train is 500m long and its speed is 100m/Sec. Find the time taken by the train to cross a poll.

Here S = 100

d= 500m/Sec

We know that s= Distance/time

So t= 500100= 5 Sec

3. Train with an object

In this type train has to cross an object like platform, Tunnel or Bridge etc. To solve this type of problem we have to use the following concept.

Let the length of the Train = L1, and the length of the Tunnel/Platform/ Bridge = L2 and time taken to cross the bridge = t and speed= s.

When the train completely,  cross the object the total length = L1 + L2

Problems on Trains

Hence the Speed (S) = Problem on trains formula

Q.3 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?

(A) 20sec

(B) 30sec

(C) 40sec

(D) 50sec

Answer: (A) 20sec

Solution: L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

Q.4 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?

(A) 20sec

(B) 30sec

(C) 40sec

(D) 50sec

Answer: (A) 20sec

Solution: L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

Q.5 A train 200m long is running at the speed 30Km/Hr. Find the time taken by the train to pass a poll near it?

(A) 9sec

(B) 3sec

(C) 4sec

(D) 8sec

Answer: (D) 8sec

Solution: L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

Theory of Relativity on Train Problems

There are two types of theory of relativity.

  1. Two Trains Moving Opposite to each other
  2. Two Trains Moving in the same Direction

4. Two Trains Crossing Each Other in Opposite Direction

Let’s assume two trains T1 and T2 of length L1 and L2 respectively. Two trains are moving in the opposite direction to each other.

Problems on Trains in Opposite Direction

Train T1’s speed is v1 and train T2’s speed is V2.

Here we have to calculate the time taken by the two train to cross each other completely.

In our case the two trains have to cross each other’s length i.e L1+L2 distance.

Let’s assume that you are travelling on a train with a speed of 80Km/Hr. You just see another train passing you at a speed of 30Km/Hr. You feel that the opposite train is moving faster than your train. While your train is moving at a faster speed. This is happening due to the addition of speed of both the train. You feel the speed of 70+30= 100Km/Hr. 

Similarly in our case speed will be considered as V1+ V2

∴ Time (t) = Problems on Trains formula

Q. Two Trains A and moving to each other at a speed of 42Km/Hr and 48 Km/Hr to  each other respectively. The length of train A is 137 meters and the length of train B is 163m. How many times they will take to cross each other?

(A) 12.0 Sec

(B) 9.0Sec

(C) 7.2 Sec

(D) 6.3 Sec

 

Answer: (A) 12.0 Sec

Solution: L1= 137m

L2= 163m

V1 = 42 Km/Hr ,

V2 = 48 Km/Hr , 

V= V1+ V2 = 42+ 48= 90Km/Hr = 90 × 5/18=  25m/Sec

T= Problems on Trains formula= 300/ 25= 12 Sec

5. Two trains moving in the Same Direction

Let’s assume train T1 and train T2 of length L1 and L2 are moving in the same direction at a speed of V1 and V2 respectively.

Problems on Trains in same Direction

Here also the length will be = L1+ L2

Let’s assume you are travelling in a train at a speed of 50Km/Hr and you find another train is moving in the same direction at the same speed. You will feel that two trains are not moving. This is due to subtraction of speed.

Similarly, in our case the overall speed can be calculated by subtracting the both train’s speed.

Speed= V1 – V2

∴ Time (t) = Problems on Trains in Same direction

Q. Two Trains A and moving in the same direction at a speed of 72Km/Hr and 54 Km/Hr to  each other respectively. The length of train A is 100m and the length of train B is 120m. How many times they will take to cross each other?

(A) 48 Sec

(B) 46 Sec

(C) 42 Sec

(D) 49 Sec

Answer: (B) 46 Sec

Solution: L1= 100m

L2= 120m

V1= 72 Km/Hr, V2= 54Km/Hr

As two trains moving in the same direction  so Relative Speed of train V= V1- V2 = 72-54 = 18 Km/Hr= 18 ×  5⁄18= 5 m/ Sec

T= (100+120)/5= 44 Sec

Problems on Trains

Q.1 A train is 150m long running on a train line at a speed of 68kmph. In what time it will cross a horse running at a speed of  8Km/Hr in the same direction?

(A) 15 Sec

(B) 14 Sec

(C) 9 Sec

(D) 12 Sec

Answer: (C) 9 Sec

Solution: Speed of the train = 68 Km/Hr

Speed of horse= 8Km/Hr

Relative speed = 68- 8= 60=68 × (5/18) = (5/30)m/ Sec

Time taken by the Train to cross the Horse = Problems on Trains= 9 Sec

Q.2 A train is running at 54Km/Hr speed and it takes 20 Sec to pass a Tonnel. Next it takes 12 Second to pass a Woman walking at 6Km/Hr in the same direction in which train is running. Find the length of the Tunnel? 

(A) 140m

(B) 200m

(C) 220m

(D) 500m

This is one of the most important Problems in Trains section.

Answer: (A) 140 m

Solution: Relative speed of train with respective to the Woman= (54-6)Km/Hr = 48 Km/Hr= 48 × (5/18) = (40/3)m/Sec

When the train will pass the Woman, the train will cover its own length with Relative speed.

∴ Length of the train = Speed × Time = (40/3) × 12= 160m

Speed of Train = 54 Km/Hr = 54 × (5/18) = 15 m/Sec

When the train will cross the Tunnel, it will cover tunnel length along with its own length.

Let the Tunnel Length be x

Speed = (Tunnel Length + Train Length) / Time

⇒20 = (x+160)/ 15

⇒ x+ 160 = 20 × 15

⇒ x= 300 – 160

⇒ x = 140

∴ The length of the Tunnel =  140m

 

Time and Work Question, Formula Tricks

Hey Guys, Welcome back to Learn Aptitude. Today I will discuss the full concept of Time Work, shortcut tricks, Formula  and I will all variant of Time and Work Questions.

In India 80% people are facing problems in Time and Work Questions. It is not so difficult, but it is a conceptual trick. Just clear your concept about Time and work and your rest work is done.

Basic Concept of Time and Work

Let us Assume there are two people, first one is Ram and Second one is Hari. In one day Ram can make 3 dolls and Hari can make 5 dolls. Now observe the following Time and Work table.

Time Ram Hari
1- Day
3 Dolls
5 Dolls
7-Days

7 × 3 =21 Dolls

7 × 5 =35 Dolls

30-Days

30 × 3 = 90 Dolls

30 × 5 = 150 Dolls 

From the above table, we can observe that Ram is taking more time than Hari for making Dolls.While Hari is producing more dolls in less time. So we can conclude that Time and work are indirectly propotional to each other.

Time and Work Formulas

  • Work Done in 1-Days= 1/Number of Days
  • Work Done in n days = Work Done in 1 Days × n days
  • Number of Days= Work Done Days/ work done in 1 days

Time and Work Questions with Answers

Q.1 A can complete a work within 6 days while B can complete that work within 5 days. If both A and B work together, then how many days, then will take to complete the same work?

(A) 10 Days
(B) 11 Days
(C) 12 Days
(D) 13 Days

Answer: (B) 11 Days

Solution: A =6 Days

B= 5 Days

L.C.M of A and B = 30

Days will be taken A and B = LCM/ A's Days + LCM/B's Days= (30/6) + (30/5)= 5 + 6= 11

∴ If A and B will work together then they will take 11 days to complete the work.

Q.2  Two People both P and Q can complete a work in 15 days and Q alone can complete the work in 20 days, then how many days P will take to complete the work?

(A) 30 Days
(B) 23 Days
(C) 60 Days
(D) 83 Days

Answer: (C) 60 Days

Solution: P+Q= 15 days

Q= 20 days

LCM of P and Q = 60

P and Q can do in 1 day= LCM/15= 4

Q can do in 1 day= LCM/20= 60/20=3

Hence P can do in 1 Day= 4-3=1

Finally, P can alone complete the work = 1 × 60= 60days

Q.3  Ram can complete a wall in 7 days of working 9 hours each while Laxman can complete in 6 days of working 7 hours each. How many days it will take if they work together 42/5?

(A) 3 Days
(B) 6 Days
(C) 9 Days
(D) 8 Days

Answer: (A) 3 Days

Solution: Ram can complete the work in 7 × 9 = 63 hours

Laxman can complete the work in 6 × 7 = 42 days

Ram's 1 hour work= 1/63

Laxman's 1 hour Work= 1/42

Both Ram and Laxman's 1 hour work will be (1/63) + (1/42)= 5/126

Hence, both will complete the work = (126/5)hrs

Days it will take to complete if they work together for 42/5 hours= (126/5) × ( 5/42) = 3 days

Q.4 Y can work twice of X. If both X and Y complete the work together within 30 days then how many days Y will take to complete the work alone?

(A) 45 Days
(B) 10 Days
(C) 58 Days
(D) 60 Days

Answer: (A) 45 Days

Solution:

 

Time and Work solutions

Q.5 Between two people A and B, B can complete a work in 20 days while A is 30% more efficient than B. How many days A will take to complete the work?

(A) 22 Days
(B) 24 Days
(C) 36 Days
(D) 38 Days

Answer: (B) 24 Days

Solution: As Per question A can work 30% more than B and we can write the ratio of their work as 120:100= 6:5

Lets assume A can complete the work within x days

Finally, we can re-write it as 6:5 :: x:20

⇒5x = 120

⇒x = 120/5= 24days

Q.6 A woman can complete a certain job in 24 days and a man can complete the same work in half the time taken by the Woman. If they work together, then how many days they will complete the work?

(A) 22 Days
(B) 15 Days
(C) 8 Days
(D) 6 Days

Answer: (C) 8 days

Solution: As per Question Woman can complete the work i 24 days 

1 day's work of man = 1/24 and

A Man can complete the work  in 24/2= 12 days.

1 day's work of woman= 1/12

Man's 1 hour Work + Woman's 1 hour Work = (1/24) + (1/12) = 3/24= 1/8

Both Man and woman will complete the work in 8/1= 8 days.

Q.7 I can paint a wall within 24 hours and with the help of my brother, I can paint it by 8 hours. If my brother will paint alone, then how many hour he will take?

(A) more than 4 days
(B) less than 4 days but greater than 3 days
(C) less than 4 days
(D) more than 4 days but less than 5 days

Answer: (D) more than 4 days but less than 5 days

Solution: I can complete the paint alone in 24 hours

1 hour's work = 1/24

With brother, I take 6 hours

1 hour's paint with my brother = 1/6

1 hour's alone paint of my brother  (1/6) - (1/24) = 5/24

Alone my brother will take time = 24/5= 4.8days

Q.8 A water tank has two holes. The first hole alone can make the water tank empty in 9 minutes where the second hole alone can make the tank empty in 6 minutes. If water flow remains at the constant rate and both the hole started to make the tank empty, then how many minutes it will take to make the tank empty.

(A) more than 4 days
(B) less than 4 days but greater than 3 days
(C) less than 4 days
(D) more than 4 days but less than 5 days

Answer: (B) less than 4 days but greater than 3 days

Solution: First tank makes the tank empty in 9 minutes

In 1 minutes it will make 1/9

Second tank makes the tank empty the in 6 minutes

In 1 minutes it will make 1/6

So, if both the holes will work at same time then in 1 minute (1/9) + (1/6) = 5/18

∴ Required time = 18/5 = 3.6

Q.9 Papu can make half sweet than Lipu in three-fourth of  the time. If they work together then they take 30 days to complete the sweet production then how many days Lipu alone will take to complete the work?

(A) 30
(B) 40
(C) 50
(D) 45

Answer: (A) 30

Solution: Let Lipu take x days to complete sweet production.

1 days work = 1/x

Lipu and Papu will complete sweet production in 30 days

In 1 days work= 1/18

Papu takes {2 × (3x/4)= 3x/2 days to complete it

As per Question we have (1/x) + (3x/2) = 1/18

By solving abopve, we have x= 30

Q.9 Papu can make half sweet than Lipu in three-fourth of  the time. If they work together then they take 30 days to complete the sweet production then how many days Lipu alone will take to complete the work?

(A) 30
(B) 40
(C) 50
(D) 45

Answer: (A) 30

Solution: Let Lipu take x days to complete sweet production.

1 days work = 1/x

Lipu and Papu will complete sweet production in 30 days

In 1 days work= 1/18

Papu takes {2 × (3x/4)= 3x/2 days to complete it

As per Question we have (1/x) + (3x/2) = 1/18

By solving abopve, we have x= 30

Q.10 Two people A and B can do a certain work in 60 days and 40 days respectively. If they both work for 6 hours, then how much fraction of the work will be completed in 6 days?

(A) 1/9
(B) 1/8
(C) 1/24
(D) 1/6

Answer: (B) 1/8

Solution: A can do the work in 60 days

In 1 day it will do 1/60 fraction

B can do the work in 40 days

In 1 days B can do 1/40 fraction

In 1 day both A and B can complete (1/60) + (1/40) = 1/24 fraction

In 4 days = (1/24) × 4= 1/8

Divisibility Rule of Numbers

Are you suffering to remembering Divisibility rule? Don’t worry, just follow this post and definitely you will remember all the rule.

Divisibility Rule

Divisibility Rule

Divisibility by 2

All numbers are divisible by 2 if its first digit from your right side (Unit Place) contains 0, 2, 4, 6 or 8. Only all, even numbers are divisible by 2.

Number Unit Place Is divisible? Cause

110

0
Yes
Its Unit Place is 0
192
2
Yes
Its Unit Place is 2
234
4
Yes
Its Unit Place is 4
366
6
Yes
Its Unit place is 6
568
8
Yes
Its Unit Place is 8
651
1
No
Its Unit Place is 1
96767
7
NO
Its Unit Place is 7

Divisibility by 3

A number is divisible by 3 only if the sum total of all the digits is divisible by 3. We have to add all the digits of that number and check whether the number is divisible by 3 or not? If Yes then the number is divisible by 3.

Number Sum of Digits Is divisible by 3? Result

78

7+8=15
Yes
As 15 is divisible by 3 So 78 is divisible
134
1+3+4=8
No
As 8 is not divisible by 3 So 134 is not divisible
261
2+6+1=9
Yes
9 is divisible by 3 So 261 is divisible
378
3+7+8=18
Yes
As 18 is divisible by 3 So 378 is divisible
6566
6+5+6+6=23
No
As 23 is not divisible by 3 SO 6566 is not divisible
46323
4+6+3+2+3= 18
Yes
As 18 is divisible by 3 So 46323 is divisible by 3

Divisibility by 4

A number is divisible by 4 if its last two digits from your right hand side is divisible by 4. 

Number Last Two Digit Is divisible by 4? Result

156

56
Yes
As 56 is divisible by 4 So 156 is divisible
242
42
No
As 42 is not divisible by 4 So 242 is not divisible
456368
68
Yes
As 68 is divisible by 4 So 456368 is divisible by 4

Divisibility by 5

If the unit digit of any number is either 0 or 5 then we can say that the number is divisible by 5. Otherwise the number is not divisible by 5.

Number Last Digit Is divisible? Result

650

0
Yes
As the unit digit is 0 So 650 is divisible by 5.
56002
2
No
As Unit digit is not 0 or 5 so it is not divisible.
79856385
5
Yes
As the unit digit is 5 So 79856385 is divisible by 5

Divisibility by 6

We can check that a number is divisible by 6 only if the number is divisible by both 2 and 3. That means we have to apply the divisibility rule of 2 and divisibility rule of 3 to and check whether the number is divisible by both or not and it must be an even number.If not the number is not divisible by 6.

A number is divisible by 6 if it is an even number and divisible by 3.

Number Is divisible by 2? Is divisible by 3? Result

96

Yes
Yes
As the number is divisible by 2 and 3 the number is divisible by 6.
256
Yes
No
The number is divisible by 2 but ot divisible by 3 So 256 is not divisible by 6
263
No
Yes
As it is an odd number it is not divisible by 6
1266
Yes
Yes
As 1266 is divisible by 2 and 3 so it is divisible by 6.

Divisibility by 7

To check the divisibility rule of 7 we have to perform the following steps:

  1. Multiply the unit digit by 2.
  2. Now subtract the multiplication result from the remaining digits.
  3. If the subtraction result is divisible by 7 then the number is divisible by 7.

Note: Use this rule till 5 digit Number.

Number Unit Digit Double of Unit Digit Subtraction Result

161

1

1 × 2= 2

(16)1= 16-2=14
As 14 is divisible by So 161 is divisible by 7
306

6

6 × 2= 12
(30)6= 30-6=24
As 24 is not divisible by 7 So 306 is not divisible by 7
693
3
3 × 2= 6
(69)3= 69-6= 63
As 63 is divisible by 7 So 693 is divisible by 7

If the number exceeds 5 digits, then do not use the above divisibility rule. Because it will be difficult for you to check the divisibility.

Divisibility Rule of 7 more than 5 Digit Number

  1. First, make pairs of 3 digits from your right hand side.
  2. Add the alternative Pairs
  3. Subtract the addition result pairs

Lets understand by taking Examples

Q. Check whether 67666662 is divisible by 7 or not?

Step-1: Make Pair of 3 digits from right side (67) -(666)-(662)

Step-2: Add Alternative Pairs 67+662= 729

Step-3: Substract from the remaining pairs. 729-666=63

Here 63 is divisible by 7 So 6766662 is divisible by 7

Divisibility by 8

If the last 3 digits from your right hand side is divisible by 8 then then the number is divisible by 8.

One initial check is that the number must be an even number, otherwise the number is not divisible by 8.

Number Last Three Digit Is divisible by 8? Result

263152

152
Yes
As 152 is divisible by 8 So 263152 is divisible
566364
364
No
As 364 is not divisible by 4 So 566364 is not divisible
5663368
368
Yes
As 368 is divisible by 8 So 5663368 is divisible by 4

Divisibility by 9

A number is divisible by 9 only if the sum total of all the digits is divisible by 9. We have to add all the digits like the divisibility rule of 3 and check whether it is divisible by 9 or not.

Number Sum of Digit Is divisible by 9? Result

6363

6+3+6+3=18
Yes
As Sum 18 is divisible by 9 SO the number is divisible by 9
96364
9+6+3+6+4=28
No
As sum is 28 which is not divisible by 9 So the number is not divisible by 9.

Divisibility by 10

Any number which has the only unit digit 0 is divisible by 10.

Number Unit Digit Is divisible by 10? Result

62610

0
Yes
As its unit digit is 0 so it is divisible by 10
554545
5
No
As its unit digit is 5 so it is not divisible by 10

Divisibility by 11

A number is diviosible by 11 if the difference between the sum of even place and sum of odd places are divisible 11 or 0.

Number Sum of Even Places Sum of Odd Places Odd-Even Result

244354

5+4+2=11
4+3+4=11
11-11=0
As the difference is 0 so the number is divisible by 11
206140
2+6+4=12
0+1+0=1
12-1=11
As the diference is 11 which is divisible by 11 SO the number is divisible by 11
636652
5+6+6=17
2+6+3=11
11-17=-6
As -6 is not divisible by 11 so the number is not divisible by 11

HCF and LCM Online Aptitude Test-1

Hey, Guys are you searching to make practice HCF and LCM Online Aptitude test? Here is the online Aptitude test of HCF and LCM. Just appear the test and make a practice of yourself.

HCF and LCM Online Aptitude Test

HCF and LCM Online Aptitude Test Details

This test contains 10 questions from the HCF and LCM sections. You have to complete your test within 15 minutes. You have to answer all the question and no skip is available.

Before Appearing the Examination Please Read the HCF and LCM Tricks and Concept

Provide your Experience and Feedback in the comment section and help us improve our Online test Series.