Question
In the question, two quantities i.e. Quantity I and
Quantity II are given. Solve the given quantities to establish the correct relation between them and choose the correct option. Quantity I: The digits at the unit and hundredth places of a three-digit number 'A' are swapped to create another three-digit number 'B'. If the difference between 'A' and 'B' is 198, and the digit at the tens place is '8', then determine the number of distinct values that 'B' can assume. Quantity II: A woman takes 15 days to complete a task. A man can accomplish the same task in 25 days. A child exhibits 50% efficiency compared to a woman. If a collective effort involving 6 children and 5 men takes '4A' days to complete the work, an effort that 12 women can accomplish in 16 days, then ascertain the value of 'A'.Solution
ATQ, Quantity I Let A = 100p + 80 + q B = 100q + 80 + p If p > q A - B = 198 (100p + 80 + q) - (100q + 80 + p) = 198 99p - 99q = 198 p - q = 2 (p, q) = (9, 7), (8, 6), (7, 5), (6, 4), (5, 3), (4, 2), (3, 1) If p < q B - A = 198 (100q + 80 + p) - (100p + 80 + q) = 198 99q - 99p = 198 p - q = 2 (q, p) = (9, 7), (8, 6), (7, 5), (6, 4), (5, 3), (4, 2), (3, 1) Number of Possible values of A = 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) × 4A = 12 × 5 × 16 (15 + 15) × A = 3 × 5 × 16 2A = 16 A = 8 Hence, Quantity I > Quantity II
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