In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. Quantity-I: The present age of Rohit is (p² - 6) years. The ratio of the age of Rohit 2 years ago to the age of Mohit 1 year hence is 4:3 respectively. If Rohit is 10 years older than Mohit, and the age of Karan is (p + 3) years more than half of the total age of Rohit and Mohit taken together, then find the average age of Rohit, Mohit and Karan. Quantity-II: 4 years ago, the age of Deepak, Neha, and Aman was (q² + 8q - 13) years, (2q² + 2) years, and (q² - 2q + 10) years respectively. If the sum of age of Neha after 6 years from now and age of Aman after 2 years from now is 78 years, then find the average of the present age of Deepak, Neha, and Aman.

Quantity I: Present age of Rohit = (p² - 6) years Present age of Mohit = (p² - 6) - 10 = (p² - 16) years ATP, {(p² - 6) - 2}/{(p² - 16) + 1} = 4/3 {(p² - 8)/(p² - 15)} = 4/3 3(p² - 8) = 4(p² - 15) 3p² - 24 = 4p² - 60

• p² + 36 = 0

p² = 36 p = 6 So, Present age of Rohit = (6² - 6) = 36 - 6 = 30 years Present age of Mohit = (6² - 6) - 10 = 36 - 6 - 10 = 20 years Present age of Karan = (30 + 20) ÷ 2 + 6 + 3 = 25 + 9 = 34 years Required average = (30 + 20 + 34) ÷ 3 = 84 ÷ 3 = 28 years So, Quantity I = 28 years Quantity II: Present age of Deepak = q² + 8q - 13 + 4 = (q² + 8q - 9) years Present age of Neha = 2q² + 2 + 4 = (2q² + 6) years Present age of Aman = q² - 2q + 10 + 4 = (q² - 2q + 14) years ATP, (2q² + 6 + 6) + (q² - 2q + 14 + 2) = 78 3q² - 2q + 28 = 78 3q² - 2q - 50 = 0 (3q + 10)(q - 5) = 0 q = 5 or -10/3 Case I: q = -10/3 Since q is not an integer, So, Case I is rejected. Case II: q = 5 Present age of Deepak = 5² + 8 × 5 - 9 = 25 + 40 - 9 = 56 years Present age of Neha = 2 × 25 + 6 = 56 years Present age of Aman = 25 - 10 + 14 = 29 years Required average = (56 + 56 + 29) ÷ 3 = 141 ÷ 3 = 47 years So, Quantity II = 47 years Hence, Quantity-I < Quantity-II