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Given below are two quantities named A and 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 answer. Quantity A: A, B and C can do a work in 24, 30 and 40 days respectively. If only A and B work for the first 6 days and then C joins them, How long will it take them to complete the work? Quantity B: B can complete the work in 20 days. C is twice as efficient as B and A takes 2 days more than it takes C to complete the work. Working together, in how much time would they be able to complete the work?

Given below are two quantities named A and 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 answer. Quantity A: A, B and C can do a work in 24, 30 and 40 days respectively. If only A and B work for the first 6 days and then C joins them, How long will it take them to complete the work? Quantity B: B can complete the work in 20 days. C is twice as efficient as B and A takes 2 days more than it takes C to complete the work. Working together, in how much time would they be able to complete the work? Correct Answer Quantity A > Quantity B

Quantity A:

Let total work = 120 units (LCM of 24, 30 and 40)

Efficiency of A = 120/24 = 5

Efficiency of B = 120/30 = 4

Efficiency of C = 120/40 = 3

Work done by A and B in 1 day = (5 + 4) = 9 units

∴ Work done by A and B in 6 days = 9 × 6 = 54 units

∴ Remaining work = 120 – 54 = 66 units

Work done by A, B and C together in 1 day = 5 + 4 + 3 = 12 units

∴ Time taken by A, B and C together to complete the remaining 66 units of work = 66/12 = 5.5 days

Quantity B:

Time taken by B to complete the work = 20 days

∴ Time taken by C to complete the work = 20/2 = 10 days

Time taken by A to complete the work alone = 10 + 2 = 12 days

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

Efficiency of A = 60/12 = 5

Efficiency of B = 60/20 = 3

Efficiency of C = 60/10 = 6

Work done by A, B and C together in 1 day = 5 + 3 + 6 = 14 units

∴ Time taken by A, B and C together to complete the work = 60/14 = 30/7 days

∴ Quantity A > Quantity B

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