Two trains, Calcutta Mail and Bombay Mail, start at the same time from stations Kolkata and Mumbai respectively towards each other. After passing each other, they take 12 hours and 3 hoursto reach Mumbai and Kolkata respectively. If the Calcutta Mail is moving at the speed of 48 km/h,the speed of the Bombay Mail isa)24 km/hb)22 km/hc)21 km/hd)96 km/hCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:

- Two trains, Calcutta Mail and Bombay Mail, start at the same time from stations Kolkata and Mumbai respectively towards each other.
- After passing each other, they take 12 hours and 3 hours to reach Mumbai and Kolkata respectively.
- Speed of Calcutta Mail = 48 km/h.

To find:

- Speed of Bombay Mail.

Solution:

Let us assume that the distance between Kolkata and Mumbai is 'd' km.

When the two trains start moving towards each other, their relative speed is the sum of their individual speeds.

- Relative speed = Speed of Calcutta Mail + Speed of Bombay Mail
- Relative speed = 48 + Speed of Bombay Mail
- Relative speed = 48 + B (let Speed of Bombay Mail be 'B')

When the two trains pass each other, they cover the entire distance between Kolkata and Mumbai.

- Total distance = d km

The time taken by Calcutta Mail to cover this distance after passing Bombay Mail is given as 12 hours.

- Time taken by Calcutta Mail = 12 hours

Using the formula:

- Speed = Distance/Time

We can write:

- Speed of Calcutta Mail = d/12

Similarly, the time taken by Bombay Mail to cover this distance after passing Calcutta Mail is given as 3 hours.

- Time taken by Bombay Mail = 3 hours

Using the formula:

- Speed = Distance/Time

We can write:

- Speed of Bombay Mail = d/3

Now, we can form another equation using the formula:

- Relative speed = Distance/Time

- Relative speed = d/(12+3)
- Relative speed = d/15

Substituting the value of relative speed in terms of B, we get:

- 48 + B = d/15

Multiplying both sides by 15, we get:

- 720 + 15B = d

Substituting this value of d in the equation for speed of Bombay Mail, we get:

- Speed of Bombay Mail = (720+15B)/3
- Speed of Bombay Mail = 240 + 5B

Now, we can substitute the value of speed of Bombay Mail in the equation for relative speed:

- Relative speed = 48 + Speed of Bombay Mail
- d/15 = 48 + 240 + 5B
- d/15 = 288 + 5B
- d = 15(288 + 5B)
- d = 4320 + 75B

Substituting this value of d in the equation for speed of Bombay Mail, we get:

- Speed of Bombay Mail = (720+15B)/3
- Speed of Bombay Mail = 240 + 5B
- Speed of Bombay Mail = 240 + 5((d-720)/15)
- Speed of Bombay Mail = 240 + (d-720)/3
- Speed of Bombay Mail = (3d-2160)/3
- Speed of Bombay Mail = d/3 - 720/3
- Speed of Bombay Mail = d/3 - 240

Substituting the value of d, we get:

- Speed of Bombay Mail = (4320 + 75B)/3 - 240
- Speed of Bombay Mail = 1440 + 25B - 240
- Speed of Bombay Mail = 1200 +

Similar Quant Doubts

Two stations P and Q are 400 km apart from each other. One train start from P at a speed of 60km/hr towards Q and after 2 hours another train starts from Q towards P at 45 km/hr. At what distance from P the train will meet.

Two stations A and B are 150 km apart from each other. One train starts from A at 6 AM at a speed of 30 km/hr and travels towards B. Another train starts from station B at 7 AM at a speed of 20 km/hr. At what time they will meet.

The distance between two cities P and Q is 300km. A train starts from station P at 10 am with speed 80 km/hr towards Q. Another train starts from Q towards P with speed 40km/hr at 11 am. At what time do they meet?

Two trains P and Q are separated by 220 km on a straight line. One train starts at 8 am from one station A towards B at 40 km/hr and another train starts from B towards A at 9 am at 60 km/hr. At what time will both train will meet?

Top Courses for Quant

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company