In the question, two Quantities I and II are given. You have to solve both the Quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. Quantity-I: 24 men can complete a work in ‘a’ days while 36 women can complete the same work in (a − 5) days. 40 men can complete the same work in ‘b’ days, while 72 women can complete the work in (b − 5) days. Find the value of ‘a’. Quantity-II: At present, the average age of Arjun and Ravi is ‘x + 8’ years, the average age of Nikhil and Ravi is ‘x + 10’ years, and the average age of Arjun and Nikhil is ‘x + 5’ years. The ratio of the present ages of Ravi and Nikhil is 16:13, respectively. If the sum of the present ages of Nikhil, Ravi, and Arjun together is 4k years, then find the value of ‘k’.

Quantity I: Let efficiency of a man and woman be ‘m’ and ‘w’ respectively, 24 X m X a = 40 X m X b (a/b) = (40/24) (a/b) = (5/3) a = 5p b = 3p ATQ; 36 X w X (a − 5) = 72 X w X (b − 5) 36 X (5p − 5) = 72 X (3p − 5) 5p − 5 = 2 X (3p − 5) 5p − 5 = 6p − 10 6p − 5p = 10 − 5 p = 5 Value of a = 5p = 25 So, Quantity I = 25 Quantity II: Let the present ages of Arjun, Ravi, and Nikhil be ‘A’ years , ‘R’ years , and ‘N’ years , respectively. ATQ; {(A + R) /2} = x + 8 A + R = 2x + 16 ...............(I) {(N + R) /2} = x + 10 N + R = 2x + 20 ..............(II) {(A + N) /2} = x + 5 A + N = 2x + 10 ..............(III) From (II) − (I): (N + R) − (A + R) = 2x + 20 − (2x + 16) N − A = 4 ..............(IV) From (III) + (IV): A + N + N − A = 2x + 10 + 4 2N = 2x + 14 N = x + 7 ...................(V) Substitute N = x + 7 in (II): (x + 7) + R = 2x + 20 R = x + 13 ..................(VI) ATQ; {(x + 13) /(x + 7)} = 16/13 13(x + 13) = 16(x + 7) 13x + 169 = 16x + 112 3x = 57 x = 19 From (V) N = x + 7 = 26 From (VI) R = x + 13 = 32 From (IV) N − A = 4 26 − A = 4 A = 22 Sum of ages: N + R + A = 26 + 32 + 22 = 80 4k = 80 k = 20 So, Quantity II = 20 Therefore, Quantity-I > Quantity-II