x boys can complete a work in 15 days and y girls can complete the

let \(x\) is number of boys, \(y\) is number of girls, \(a\) is boy rate , \(b\) is girl rate.
number of workers * rate * days = work

given:\(x*a*15 = y*b*24 = 1\) ---> so we have 4 variables

from statement 1: \(a = 2b\) & \(x+y = 27\)

\(x*2b*15\) = \(y*b*24\)
\(30x = 24y\) , \(x+y = 27\) ---> (from the two equations, we can find x & y, and we can further find a & b) ---> sufficient

from statement 2: if \(x = y\), then days needed by boys (let it m) = \(\frac{1}{2}\) days needed by girls (let it n) or\(m = \frac{1}{2}n\)

\(x*a*m\) = \(y*b*n\)
\(a = 2b\) --> (ratio between rate of boys and girls) (same as info 1 from statement 1)
which means that \(30x = 24y\) --> (ratio between number of boys and girls)

However, the ratios can't provide the values of x,y,a,b
(actually statement 2 provided only one of the two infos of statement 1) ---> insufficient

so A