Two buses start from opposite points on a man road, 120 km apart. The first bus X runs for 25 kms and takes a right turn and runs for another 15 kms. It then turns left and runs for another 25 kms and takes the direction back to reach the main road. In the mean time, due to minor breakdown, the other bus Y has run only 35 kms along the main road. What would be the distance between the two buses at his point ?

Options

A. 35 kms
B. 45 kms
C. 50 kms
D. 55 kms

Explanation

To solve the problem step by step, we can break down the movements of both buses and calculate the distance between them.

### Step 1: Understand the initial positions of the buses
- The two buses start 120 km apart on a straight road. Let's denote the starting point of Bus X as point A and the starting point of Bus Y as point B.
- The distance between A and B is 120 km.

**Hint:** Visualize the positions of the buses on a straight line.

### Step 2: Analyze the movements of Bus X
- Bus X travels 25 km forward from point A.
- After this, it takes a right turn and travels 15 km downwards (perpendicular to the main road).
- Then, it takes a left turn and travels 25 km to the left (parallel to the main road) before heading back to the main road.

**Hint:** Draw a diagram to track Bus X's movements step by step.

### Step 3: Determine the final position of Bus X
- After moving 25 km forward, Bus X is now at point C (25 km from A).
- After the right turn and moving 15 km downwards, Bus X is at point D (25 km, 15 km down).
- After the left turn and moving 25 km, Bus X is now at point E (0 km, 15 km down from the main road).
- Finally, Bus X returns to the main road, which means it goes back up 15 km to reach the main road.

**Hint:** Keep track of the coordinates of Bus X after each movement.

### Step 4: Analyze the movements of Bus Y
- Bus Y travels 35 km forward along the main road from point B.

**Hint:** Mark the position of Bus Y on the same diagram.

### Step 5: Calculate the distance between the two buses
- At this point, Bus X is directly above the main road (0 km, 0 km) and Bus Y is 35 km from point B (which is at 120 km).
- The position of Bus Y is at point F (120 km - 35 km = 85 km from point A).

**Hint:** Use the distance formula to find the distance between the two buses.

### Step 6: Calculate the distance
- The distance between Bus X (0 km) and Bus Y (85 km) is:
\[ \text{Distance} = 120 \text{ km} - (25 \text{ km} + 25 \text{ km} + 35 \text{ km}) = 120 \text{ km} - 85 \text{ km} = 35 \text{ km} \]

### Final Answer
The distance between the two buses is **35 km**.

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