Time, Distance and Train Problems

This is the major topic in any competitive examinations. So, I am now explaining the shortcut and the fastest method for solving these problems. There are four different types of problems in this topic.
They are:          1. Problems on Time taken by train

2. Problems on Distance covered by train

3. Problems on speed of train

4. Problems on 2 trains in same direction

5. Problems on 2 trains in opposite direction

6. Problems on finding Length of train or platform

7. Problems on platform crossing time

8. Average speeds

  You all know this basic Triangle.

/\

/  D \

/ T |  S \

D – Distance , T – Time,  S – Speed , L – length of train, Lp – Platform length

 Where d=t *s

                T= d/s

                S= d/t

Time calculated when distance and speed is given          :               t=d/s

                                When length (l) and speed is given         :        t= l/s      (pole/man crossing time)

Time taken to cross platform     :               (L+Lp)/s

Relative speeds                               : Same direction = (S1 – S2)         ; (where s1 >s2)

                                                : Opposite direction = (S1+S2)

Time taken by trains cross in same direction is (sum of lengths of trains / diff in speeds)

Time at which 2 trains pass by is (Sum of lengths / sum of speeds)

Important NOTE:

Conversions:                     18 kmph = 5mps

                10 mts --->1kmph ---> 36 sec

                                20 mts ---> 2kmph ---> 36 sec

                                30 mts ---> 3kmph ---> 36 sec and so on..

Ie, a vehicle travels 10 meters distance with 1kmph speed in 36 seconds

Vehicle travels 20 meters distance with 2kmph speed in 36 seconds

Vehicle travels 30 meters distance with 3kmph speed in 36 seconds

Vehicle travels 40 meters distance with 4kmph speed in 36 seconds and so on..

Now, we will see how to use the above shortcut.

A car travels with a speed of 108kmph. What distance will be covered in 15 sec?

Ans : 450mts

Solution: Write the given parameters in above format

1080mts --> 108 kmph ---> 36sec

Now we know distance travelled in 36 sec. Find 15sec distance using this.

Ie by Ratio method as i already mentioned in my previous posts Ratio and Proportion

                36 --> 1080

                15 --> ??                (450)

Average speeds:

When distance is constant ie speeds are given  :               2ab/ (a+b)

When distances and times are given                  :               Total distance/ Total time

Try some problems and Answer them:

                         

1.90kmph in m/s

2.52m/s in kmph

3.A vehicle covers a distance of 600mts in 2 mins. What is Speed in kmph

4.A car runs at 78kmph. What is the distance covered in 1min 12 sec?

5.At what time car travels over a distance of 420mts, if it runs at 90kmph?

6.The ratio between two trains’ speeds is 7:8. If second train runs 400kmph in 5hrs, the speed of first train is?

7.Speeds of A and B are in ration 3:4. A takes 20 mins more than B to reach the destination. Then What is time taken by A and B to reach the destination?

 Back to you soon...

Solved Numerical Aptitude Questions

Question 1: The sum of the ages of husband and wife is 70 years and the ratio of their age is 3 : 2. The age of the wife is:

1. 32 years 
2. 25 years

3. 28 years

4. 27 years
5.

Correct Answer: 3.


Question 2: A trader would incur a loss of 15%, if he sells pens at 10.20 per pen. If 12.5% profit is to be earned after allowing 10% discount on the marked price then find the marked price. ?

1. 20
2. 1.5
3. 150
4. 12
5. 15

Correct Answer: 5.


Question 3: A shopkeeper sells sugar at 4% less than market price, but gives weight 800 grams instead of 1 Kg. What is the profit percentage overall?

1. 5%
2. 10%
3. 20%
4. 25%
5. 12%

Correct Answer: 3.


Question 4: What is the location of the atomic power station?

1. Mumbai
2. Tarapore
3. Kalpakkam
4. Kaiga
5.

Correct Answer: 2.


Question 5: A shirt was sold at a profit of Rs.50. If a trouser was sold at half the profit percenta9e and the cost price of the trouser is thrice that of the shirt, find the profit made on the trouser (in Rs.)

1. 25
2. 57
3. 75
4. 50
5.

Correct Answer: 3.


Question 6: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches, the batsman scored an average of 13 runs. Find his average in all the 30 matches.

1. 27
2. 26
3. 31
4. 29
5.

Correct Answer: 3.


Question 7: 729 ml of a mixture contains milk and water in ratio 7 : 2. How much more water is required to be added to get a new mixture containing milk and water in the ratio of 7 : 3?

1. 60 ml
2. 70 ml
3. 81 ml
4. 90 ml
5.

Correct Answer: 3.


Question 8: What is the difference between the simple interest and the compound interest on a sum of 4700 at 20% p.a. for a period of 2 years ?

1. Rs.190
2. Rs.188
3. Rs.196
4. Rs.199
5.

Correct Answer: 2.


Question 9: If a trader sold two cars each at 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?

1. 14.48% loss
2. 14.4% loss
3. 14.4% profit
4. 1.44% loss
5.

Correct Answer: 2.


Question 10: A trader wants to sell a watch at 25% profit. If its cost price was Rs.x more, an extra profit of 50.would be made on it. Find x (in Rs.)

1. 100
2. 125
3. 130
4. 145
5. 200

Correct Answer: 5.


Question 11: In how many years does a sum of Rs.5000 give a simple interest of Rs.16500 at 15°, p.a.?

1. 22
2. 24
3. 25
4. 23
5.

Correct Answer: 1.


Question 12: A certain sum becomes Rs.20720 in 4 years and 24080 in 6 years at simple interest. Find sum and rate of interest.

1. Rs.12000; 12% p.a
2. Rs.14000; 12% p.a
3. Rs.12000; 15% p.a
4. Rs.14000; 15% p.a
5.

Correct Answer: 2.


Question 13: Francis and George started a business with investments of Rs.7000/- and Rs.10000/-. After x months, Francis left. After two more months David joined the business with an investment of Rs.10000/-. If the annual profit is shared among David, Francis and George in the ratio 10 : 7 : 24, find the respective time periods of David, Francis and George for which they stayed that year.

1. 5:5:12
2. 1:1:3
3. 1:1:4
4. 1:1:2
5.

Correct Answer: 3.


Question 14: 89.447+98.3+67.77=_____________

1. 254.417
2. 250.146
3. 254.369
4. 2549369
5. 255..517

Correct Answer: 5.


Question 15: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining is 90. Find the number of students who wrote the exam.

1. 15
2. 20
3. 25
4. 35
5.

Correct Answer: 3.


Question 16: The difference between 38% of number and 24% of the same number is 135.10. what is 40% of that number ?

1. 394
2. 370
3. 378
4. 386
5. None of these

Correct Answer: 4.


Question 17: 29.299+5.55+68.7=____________________________

1. 104.236
2. 123.569
3. 103.549
4. 124.263
5. 25.25521

Correct Answer: 3.


Question 18: A and B can do a work in 20 and 30 days respectively. They started the work together, but A left after some time and B finished the remaining work in 5 days. Then what is the number of days after which A left?

1. 5
2. 10
3. 12
4. 15
5. None of these

Correct Answer: 2.


Question 19: Avinash purchases five cycles at the rate of Rs 450 per cycle. He spends Rs 150 on each cycle for repairs. At what price he should sell them to gain a profit of 35%?

1. Rs 600
2. Rs 750
3. Rs 608
4. Rs 810
5.

Correct Answer: 4.


Question 20: A sold an article to B at 10% profit and B sold it to C at 15% profit. If B purchased for Rs.220/-, then find the difference in the purchasing prices for A and C.

1. 35
2. 53
3. 45
4. 78
5.

Correct Answer: 2.


Question 21: A shopkeeper sold an Air-conditioner for Rs 25,935 with a discount of 9% and earned a profit of 3.74%. What would have been the percentage of profit earned if no discount were offered?

1. 15.6%
2. 16% 
3. 12.3%
4. None of the above
5.

Correct Answer: 4.


Question 22: Two equal glasses are respectively 1/4 and 3/4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. The ratio of milk and water in the tumbler is:

1. 3 : 11
2. 7 : 17
3. 9 : 23
4. 11 : 23
5.

Correct Answer: 2.


Question 23: Pick the odd number from the series - 11, 12, 8, 27, 10.75, 56.5

1. 12
2. 8
3. 27
4. 10.75
5. 56.5

Correct Answer: 5.


Question 24: 9.75 + 25.88 + ? = 41.18

1. 5.55
2. 5.75
3. 6.57
4. 4.23
5.

Correct Answer: 1.


Question 25: The value of a machinery decreases by 20% p.a. on the value at the beginning of every year. The value of the machinery after 2 years will be Rs.23526,40. What is the present value of the machinery?

1. Rs.36770
2. Rs.36750
3. Rs.36740
4. Rs.36760
5.

Correct Answer: 2.