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: A can complete a work in 10 days and B can complete the same work in 15 days. If they work together, in how many days will they complete the work? Quantity II: C can complete a work in 12 days and D can complete the same work in 24 days. If they work together, in how many days will they complete the work?

For Quantity I: ATQ, Time taken by A to complete the work = 10 days. Time taken by B to complete the work = 15 days. Or, 1 day's work of A = 1/10. 1 day's work of B = 1/15. So, 1 day's work of A and B together = 1/10 + 1/15 = (3 + 2)/30 = 5/30 = 1/6. Thus, time taken by A and B together = 6 days. For Quantity II: ATQ, Time taken by C to complete the work = 12 days. Time taken by D to complete the work = 24 days. Or, 1 day's work of C = 1/12. 1 day's work of D = 1/24. So, 1 day's work of C and D together = 1/12 + 1/24 = (2 + 1)/24 = 3/24 = 1/8. Thus, time taken by C and D together = 8 days. Comparing both quantities: Quantity I = 6 days Quantity II = 8 days Clearly, Quantity I < Quantity II. Hence, the correct answer is B.