Select the correct answerTwo trains start at the same time from A & B and proceed towards B & A at 36 kmph & 42 kmph respectively. When they meet, it is found that one train has moved 48 km more than the other. What is the distance between A and B?Options624 km544 km460 km636 km

Sure, here is the step by step solution:

Step 1: Let's denote the distance that the first train travels as D1 and the distance that the second train travels as D2.

Step 2: We know that the speed of the first train is 36 kmph and the speed of the second train is 42 kmph.

Step 3: We also know that when the two trains meet, one train has traveled 48 km more than the other. This means that D2 = D1 + 48.

Step 4: The time it takes for the two trains to meet is the same for both trains. So, we can set up the equation D1/36 = D2/42.

Step 5: Substitute D2 = D1 + 48 into the equation: D1/36 = (D1 + 48)/42.

Step 6: Solve this equation for D1. You will get D1 = 288 km.

Step 7: Substitute D1 = 288 km into the equation D2 = D1 + 48 to find D2. You will get D2 = 336 km.

Step 8: The distance between A and B is the sum of the distances that the two trains traveled, which is D1 + D2 = 288 km + 336 km = 624 km.

So, the correct answer is 624 km.

To solve this problem, we can use the concept of relative speed.

Step 1: Calculate the relative speed of the two trains. Since they are moving towards each other, we add their speeds together. So, the relative speed is 36 kmph + 42 kmph = 78 kmph.

Step 2: We know that one train has travelled 48 km more than the other. This means that the trains must have been travelling for the time it takes for one train to cover 48 km at the relative speed of 78 kmph. So, the time = distance/speed = 48 km / 78 kmph = 0.6154 hours.

Step 3: Now, we can find the distance each train travelled in this time. The first train travelled at 36 kmph for 0.6154 hours, which is 36 kmph * 0.6154 hours = 22.15 km. The second train travelled at 42 kmph for 0.6154 hours, which is 42 kmph * 0.6154 hours = 25.85 km.

Step 4: The total distance between A and B is the sum of the distances each train travelled, which is 22.15 km + 25.85 km = 48 km.

So, the correct answer is 48 km. However, none of the options provided match this answer. There might be a mistake in the problem or the options provided.