Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM. Train B

First, we shall find when & where will B catch up to A:
As A moved 3 hours earlier, the distance between them was 60*3 = 180 km
The time needed by B to catch up to A = \(\frac{180}{90-60} = 6\) hours
In 6 hours, Train B will have traveled 90*6 = 540 km

So the left distance that Train C should have traveled to meed A & B = 1260 - 540 = 720 km

As train B & C started traveling at the same time, C must have traveled for 6 hours same as B.
so the speed of C = \(\frac{720}{6}\) = 120 km/h

90(t-3)=60t
30t=270
t=9,60×9=540
So trains A and B, travel 540 kms of 1260 distance between Delhi and Numbai.
1260-540=720
Because C travels at 9,so
720=6v ==》v=120
Option A

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If at distance d from Mumbai they meet and s speed of train C

d/60 = d/90+3 = (1260-d)/s + 3

From 1st eqn, d = 540 km.
so 540/60 = (1260-540)/s +3
=> s = 720/6 = 120kmph

Given:
1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM.
2. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM.
3. Train C leaves Delhi for Mumbai at 9PM.
4. All the trains meet at the same time between Mumbai and Delhi
5. The distance between Delhi and Mumbai is 1260 kms

Asked: What is the speed of train C ?

Let the speed of train C be x.

1. Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 PM.
2. Train B travelling at 90km/ he also leaves Mumbai for Delhi at 9 PM.

Train A travel from 6PM to 9PM = 60 *3 = 180 km

4. All the trains meet at the same time between Mumbai and Delhi
Train A & Train B meet at = 180/(90-60) = 6 hours after 9PM
Train B travels = 90*6 = 540 km from Mumbai to Delhi at the time of meeting.

5. The distance between Delhi and Mumbai is 1260 kms
Train distance travelled by train C from Delhi to Mumbai = 1260 - 540 = 720 km
Time taken by train C = 6 hours
Speed of train C = 720/6 = 120 kmh

IMO A

Step 1: Find the Time and Distance from Mumbai at which/where B catches up with A


Let the Time when they all Meet after 9 P.M. be = T

A ----- 60 * (T + 3) = Distance A travels to Meet
B ---- 90 * (T) = Distance B travels to Meet

60*(T + 3) = 90 * T
180 = 30 * T

Time = 6 hours after 9 PM train B catches up to train A to the Meeting Point

Since C leaves at 9 PM also and all 3 Trains meet at the SAME TIME and at the Same Meeting Point, Train C will also take 6 hours after 9 PM to meet B and A

Train B travels a Distance = 90 km/hr * 6 hours = 540 km to get to the Meeting Point

Since C is coming from the Opposite Direction towards B and A, it must be True that C makes up the remaining Distance in 6 hours ---- Total Distance of 1, 260 km - 540 km that B and A traveled to the Meeting Point

Speed of C = (1, 260 km - 540 km) / 6 hours

Speed of C = 720 / 6 = 120 km per hour

Answer -A-

Solution:

When all three trains meet at the same time, train B meets (i.e., catches up with) train A when they both meet train C coming from the opposite direction. Therefore, we need to figure out what time train B catches up with train A. We can create the equation where t is the number hours it takes for train B to catch up with train A after train B leaves Mumbai:

60(t + 3) = 90t

60t + 180 = 90t

180 = 30t

6 = t

Thus, it takes 6 hours for train B to catch up with train A, and during this time period, it has traveled 90 x 6 = 540 km. Since the distance between Mumbai and Delhi is 1260 km, it must mean train C travels 1260 - 540 = 720 km in 6 hours. Therefore, the speed of train C is 720/6 = 120 km/h.

Answer: A
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