Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: A and B together, B and C together and C and A together can complete a piece of work in 10, 12 and 20 days respectively. In how many days can B finish the work alone?
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?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