The question consists of two statements numbered "I and

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.