Given below are two quantities named A and B. Based on the information, you have to determine the relationship between two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A work can be complete by P and Q in 12 days, Q and R in 15 days, R and P in 30 days. In how many days, P alone can finish the work? Quantity B: A work can be complete by P and Q in 16 days, Q and R in 12 days, R and P in 32 days. In how many days, P alone can finish the work?

Given below are two quantities named A and B. Based on the information, you have to determine the relationship between two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A work can be complete by P and Q in 12 days, Q and R in 15 days, R and P in 30 days. In how many days, P alone can finish the work? Quantity B: A work can be complete by P and Q in 16 days, Q and R in 12 days, R and P in 32 days. In how many days, P alone can finish the work? Correct Answer Quantity A < Quantity B

Solving for Quantity A:

According to question,

(P + Q)’s 1 day’s work = 1/12     ----(i)

(Q + R)’s 1 days’ work = 1/15     ----(ii)

(R + p)’s 1 day‘s work = 1/30     ----(iii)

On adding equations (i), (ii) and (iii), we get

2(P + Q + R)’s 1 days’ work = 1/12 + 1/15 + 1/30 = (5 + 4 + 2)/60 = 11/60

⇒ (P + Q + R)’s 1 day‘s work = 11/120

P’s 1 days’ work = 11/120 - 1/15 = 1/40

Hence, P alone will complete the work in 40 days

Quantity A = 40 days

Solving for Quantity B:

According to question,

(P + Q)’s 1 day’s work = 1/16     ----(i)

(Q + R)’s 1 days’ work = 1/12     ----(ii)

(R + p)’s 1 day‘s work = 1/32     ----(iii)

On adding equations (i), (ii) and (iii), we get

2(P + Q + R)’s 1 days’ work = 1/16 + 1/12 + 1/32 = 17/96

⇒ (P + Q +R)’s 1 day‘s work = 17/192

P’s 1 days’ work = 17/192 - 1/12 = 1/192

Hence, P alone will complete the work in 192 days

Quantity B = 192 days