'Armaan' and 'Bittu' are traveling from points 'P' and 'Q,' respectively, toward each other. 'Armaan' reaches point 'Q' in 12 hours, while 'Bittu' takes 12.5 hours to reach point 'P' after meeting 'Armaan.' Quantity-I: Calculate the difference in time taken by 'Armaan' and 'Bittu' to reach their respective destinations. Quantity-II: Determine the time taken by 'Armaan' to reach the meeting point.

ATQ, Let the meeting point of 'Armaan' and 'Bittu' be point 'a'. Let the time taken by both 'Armaan' and 'Bittu' to reach point 'a' be 't' hours. Time taken by 'Armaan' to reach point 'Q' after reaching point 'a' = '12 - t' hours And time taken by 'Bittu' to reach point 'P' after meeting 'Armaan' = 12.5 hours ATQ, [(12-t)/t] = (t/12.5) 150 - 12.5t = t² Since, time cannot be negative, t = 7.5 Quantity I: So, total time taken by 'Bittu' to reach point 'P' = 7.5 + 12.5 = 20 hours So, required difference = 20 - 12 = 8 hours So, Quantity I = 8 hours Quantity II: Time taken by 'Armaan' to reach the meeting point = 7.5 hours So, Quantity II = 7.5 hours So, Quantity I > Quantity II