Each question below contains a statement followed by Quantity I and Quantity
II. Compare the value derived from Quantity I and Quantity II and choose the correct option. Quantity I: Number of days taken by P alone to complete a work. Quantity II: 15 days. Information: P and Q together can complete the work in 10 days, Q and R together can complete the work in 12 days, and R alone can complete the work in 30 days. Which of the following options correctly represents the relationship between Quantity I and Quantity II?

Let the daily work rates of P, Q, and R be p, q, and r respectively. ATQ, P and Q together can complete the work in 10 days: p + q = 1/10 ... (i) And, Q and R together can complete the work in 12 days: q + r = 1/12 ... (ii) And, R alone can complete the work in 30 days: r = 1/30 ... (iii) From (ii) and (iii), we get: Or, q + 1/30 = 1/12 Or, q = 1/12 - 1/30 Or, q = (5 - 2)/60 = 3/60 = 1/20 Now, substituting the value of q in (i): Or, p + 1/20 = 1/10 Or, p = 1/10 - 1/20 = 1/20 So, time taken by P alone to complete the work = 1 ÷ (1/20) = 20 days. Thus, Quantity I = 20 days and Quantity II = 15 days. Therefore, Quantity I > Quantity II. Hence, the correct answer is A.