Quantity I:  A three-digit number 'x' is transformed into another three-digit number 'y' by swapping the digits at the unit and hundredth places. The difference between 'x' and 'y' is 198, and the digit in the tens place remains 8. How many different values can 'x' take? Quantity II:  A girl can complete a task in 15 days, while a boy takes 25 days to finish the same task. A child's efficiency is 50% that of a girl. If a group consisting of 6 children and 5 boys takes 4x days to complete a task that 12 girls can finish in 16 days, determine the value of 'x'.

ATQ, Quantity I, Let x = 100a + 80 + b y = 100b + 80 + a If a > b x - y = 198 (100a + 80 + b) - (100b + 80 + a) = 198 99a - 99b = 198 a - b = 2 (a, b) = (9, 7), (8, 6), (7, 5), (6, 4), (5, 3), (4, 2), (3, 1) If a < b y - x = 198 (100b + 80 + a) - (100a + 80 + b) = 198 99b - 99a = 198 b - a = 2 (b, a) = (9, 7), (8, 6), (7, 5), (6, 4), (5, 3), (4, 2), (3, 1) Number of Possible values of x = 7 + 7 = 14 Quantity II, Woman -->  15                 5                            } 75 { Man  -->       25                 3 Efficiency of Child = 5 × 0.5 = 2.5 (6 × 2.5 + 5 × 3) × 4x = 12 × 5 × 16 (15 + 15) × x = 3 × 5 × 16 2x = 16 x = 8 Quantity I > Quantity II