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:

Here's a brief explanation:

1. Analyze Statement 1: They take 5 hours to meet.

   • Person X walks at a uniform speed of 1.5 km/hr. In 5 hours, X covers a distance of 5 hours * 1.5 km/hr = 7.5 km.
   • Person Y's speeds are 1 km/hr (1st hr), 1.25 km/hr (2nd hr), 1.5 km/hr (3rd hr), 1.75 km/hr (4th hr), and 2 km/hr (5th hr).
   • In 5 hours, Y covers a total distance of 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km.
   • The total distance covered by X and Y together in 5 hours is 7.5 km + 7.5 km = 15 km.
   • Since the total distance between A and B is 15 km, they meet in exactly 5 hours. Thus, statement 1 is correct.

2. Analyze Statement 2: They meet midway between A and B.

   • The total distance is 15 km. Midway would be at 15 km / 2 = 7.5 km from either A or B.
   • From the calculation for statement 1, X covers 7.5 km and Y covers 7.5 km when they meet.
   • Since X starts from A and covers 7.5 km, the meeting point is 7.5 km from A.
   • Since Y starts from B and covers 7.5 km, the meeting point is 7.5 km from B.
   • Both distances are exactly half of the total distance, meaning they meet midway. Thus, statement 2 is correct.

Since both statements 1 and 2 are correct, the correct answer is C.

The final answer is C