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 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.

Correct Option (3)

The total distance separating places A and B is 15 km.

• Person X walks at a constant speed of 1.5 km/hr.
• Person Y's speed increases hourly:
  • 1st hour: 1 km/hr
  • 2nd hour: 1.25 km/hr
  • 3rd hour: 1.5 km/hr
  • 4th hour: 1.75 km/hr
  • 5th hour: 2 km/hr

To determine if they meet in 5 hours:

• Distance covered by X in 5 hours = Speed of X × Time = 1.5 km/hr × 5 hours = 7.5 km.
• Distance covered by Y in 5 hours = Sum of distances covered each hour = 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km.

The total distance covered by both X and Y when walking towards each other for 5 hours is 7.5 km + 7.5 km = 15 km. This sum equals the initial separation distance between A and B. Therefore, they meet after 5 hours, making Statement 1 correct.

To determine if they meet midway:

Since both X and Y have covered exactly 7.5 km each, and the total distance is 15 km, they meet at the midpoint of the journey. The midpoint is 15 km / 2 = 7.5 km from either A or B. Thus, Statement 2 is also correct.

As both Statement 1 and Statement 2 are correct, option 3 is the correct answer.

Incorrect Options:

Options 1, 2, and 4 are incorrect because the calculations demonstrate that both statements are factually accurate. Statement 1 correctly identifies the meeting time as 5 hours, and Statement 2 correctly identifies the meeting point as midway between A and B, as each person covers 7.5 km in 5 hours.