Question
The question consists of two statements numbered "I and
II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Find the time taken by 'K' and 'L' together to complete the work. 'L' is 28(4/7)% less efficient than 'K'. Statement I: For the same time, 5 times the work done by 'K' is equal to 7 times the work done by 'L'. Statement II: 'K' alone does (4x 2  + 18x + 3 2  - 6x) % of the total work in (2x + 3) 2  days.Solution
Let the efficiency of 'K' = 7x units/day
Then, efficiency of 'L' = 7x X (5/7) = 5x units/day
Statement I:
5 X work done by 'K' = 7 X work done by 'L'
Or, 5 X 7x = 7 X 5x
Or, 35x = 35x
So, data in statement I alone is not sufficient to answer the question.
Statement II:
Time taken by 'K' to complete the whole work alone:
= (2x + 3) 2  X {100 ÷ (4x 2  + 18x + 3 2  - 6x) }
= (2x + 3) 2  X {100 ÷ (4x 2  + 12x + 9) }
= (2x + 3) 2  X {100 ÷ (2x + 3) 2 } = 100 days
So, total work = 100 X 7x = 700x units
So, time taken by K and L together to complete the work:
= 700x ÷ (5x + 7x)
= 700x ÷ 12x = 58(1/3) days
So, data in statement II alone is sufficient to answer the question.
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