Four persons A B C and D are hired to do work A C and D can complete the task in 16 days while worki...........

Quantitative Aptitude ( CCS) Data Sufficiency

Four persons A,B,C and D are hired to do work. A, C and D can complete the task in 16 days while working together. Find the number of days taken by B alone to complete the task.

Statement I: C and D can complete the task in 24 days, B is 100% more efficient than A.

Statement II: A alone can complete the work in 48 days and ratio of efficiency of C and D is 1:2 resp.

Either I or II

Only Statement I

Both are not sufficient

Only Statement II

Both are necessary

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Explanation:

From I: Let the total work lcm(16,24) = 48 units

Work done by A,C and D in one day = 48/16 = 3 units

Work done by C and D in one day = 48/24 = 2 units
Work done by A in one day = 3-2 = 1 unit
Therefore, number of days taken by A to complete the work = 48/1 = 48 days
The time taken by B to complete the work = 48/2 = 24 days
This statement is alone sufficient.
From II: Let the efficiency of C and D be x and 2x resp.
1/48 + x + 2x = 1/16
=>x = 1/72
This statement is not sufficient to answer.

Hence, option 2 is the correct answer.