Quantity B: P & Q working alone can complete a wok in 20 and 30 days r

1.	Quantity B: P & Q working alone can complete a wok in 20 and 30 days respectively. They started together but after 9 days P left, in how many days will the total work be completed?1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B
Answer» Quantity A: Let total UNITS of WORK = 60 units (LCM of 10, 12 and 20) ∴ Efficiency of A and B together = 60/10 = 6 Efficiency of B and C together = 60/12 = 5 Efficiency of C and A together = 60/20 = 3 ∴ Efficiency of A, B and C together = (6 + 5 + 3)/2 = 7 ∴ Efficiency of B = 7 – 3 = 4 ∴ Time taken by B to finish the work alone = 60/4 = 15 days Quantity B: Let total units of work = 60 units (LCM of 20 and 30) ∴ Efficiency of P = 60/20 = 3 Efficiency of Q = 60/30 = 2 Since P left after 9 days; Unit of work left after 9 days = 60 – 9 × (3 + 2) = 15 units ∴ Time taken by Q to finish the remaining work = 15/2 = 7.5 days ∴ Total time to finish the work = 9 + 7.5 = 16.5 days ∴ Quantity B > Quantity A

Quantity B: P & Q working alone can complete a wok in 20 and 30 days respectively. They started together but after 9 days P left, in how many days will the total work be completed?1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Quantity A:

Let total UNITS of WORK = 60 units (LCM of 10, 12 and 20)

∴ Efficiency of A and B together = 60/10 = 6

Efficiency of B and C together = 60/12 = 5

Efficiency of C and A together = 60/20 = 3

∴ Efficiency of A, B and C together = (6 + 5 + 3)/2 = 7

∴ Efficiency of B = 7 – 3 = 4

∴ Time taken by B to finish the work alone = 60/4 = 15 days

Quantity B:

Let total units of work = 60 units (LCM of 20 and 30)

∴ Efficiency of P = 60/20 = 3

Efficiency of Q = 60/30 = 2

Since P left after 9 days;

Unit of work left after 9 days = 60 – 9 × (3 + 2) = 15 units

∴ Time taken by Q to finish the remaining work = 15/2 = 7.5 days

∴ Total time to finish the work = 9 + 7.5 = 16.5 days

∴ Quantity B > Quantity A