A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1.5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1.25 km/hr in the second hour and with a uniform speed of 1.5 km/hr in the third hour and so on.

Which of the following is/are correct?

1. They take 5 hours to meet.

2. They meet midway between A and B.

Select the correct answer using the code given below:

The correct answer is Both 1 and 2.

Step 1: Understand the speeds and distances covered by person X and person Y.

The distance between place A and place B is 15 km.

Person X walks at a uniform speed of 1.5 km/hr every hour.

Person Y's speed increases by 0.25 km/hr each hour:

• Hour 1: Speed of Y = 1 km/hr
• Hour 2: Speed of Y = 1.25 km/hr
• Hour 3: Speed of Y = 1.5 km/hr
• Hour 4: Speed of Y = 1.75 km/hr
• Hour 5: Speed of Y = 2 km/hr

Step 2: Calculate the distance covered by X and Y hour by hour.

In Hour 1:
• Distance by X = 1.5 km
• Distance by Y = 1 km
• Total distance covered in 1 hour = 1.5 + 1 = 2.5 km

In Hour 2:
• Distance by X = 1.5 km
• Distance by Y = 1.25 km
• Total distance covered in 2nd hour = 1.5 + 1.25 = 2.75 km

In Hour 3:
• Distance by X = 1.5 km
• Distance by Y = 1.5 km
• Total distance covered in 3rd hour = 1.5 + 1.5 = 3 km

In Hour 4:
• Distance by X = 1.5 km
• Distance by Y = 1.75 km
• Total distance covered in 4th hour = 1.5 + 1.75 = 3.25 km

In Hour 5:
• Distance by X = 1.5 km
• Distance by Y = 2 km
• Total distance covered in 5th hour = 1.5 + 2 = 3.5 km

Step 3: Verify Statement 1 (Time taken to meet).

Total distance covered in 5 hours:

$\text{Total Distance}=2.5+2.75+3+3.25+3.5=15\text{km}$

Since the total distance covered in 5 hours equals the initial distance of 15 km between A and B, they take exactly 5 hours to meet. Therefore, Statement 1 is correct.

Step 4: Verify Statement 2 (Meeting location).

The total distance walked by X in 5 hours is:

$\text{Distance by X}=5\times 1.5=7.5\text{km}$

The total distance walked by Y in 5 hours is:

$\text{Distance by Y}=1+1.25+1.5+1.75+2=7.5\text{km}$

Since the total distance between A and B is 15 km, the midpoint is at 7.5 km. Both X and Y walk exactly 7.5 km before meeting, which means they meet midway between A and B. Therefore, Statement 2 is correct.

Both statements 1 and 2 are correct.