NTSE Stage 2 MAT 2014 Question Paper

From statement I
$\frac{1}{2}\mathrm{C}=\mathrm{A}$
C = 2A
b Now let A can complete a work in y day
∴ C = 2y
Now A, B and C together can complete a work in x day.
∴ B’s one day work
$=\frac{1}{\mathit{x}}-\left(\frac{1}{\mathit{y}}+\frac{1}{2\mathit{y}}\right)$
$=\frac{1}{\mathit{x}}-\frac{3}{2\mathit{y}}=\frac{2\mathit{y}-3\mathit{x}}{2\mathit{x}\mathit{y}}$
So B can do a work in $\frac{2\mathit{x}\mathit{y}}{2\mathit{y}-3\mathit{x}}$ day
From statement II
$\mathrm{A}+\mathit{C}=\frac{1}{2}\mathrm{B}$
B = 2(A + C)
Let A & C together can complete in m days
∴ B = 2m days
From statement III
A and C taken together can complete the work in ‘z’ day
∴ B’s one day work $=\frac{1}{\mathit{x}}-\frac{1}{2}=\frac{\mathit{z}-\mathit{x}}{2\mathit{x}}$
∴ B can complete the work in $\frac{2\mathit{x}}{\mathit{z}-\mathit{x}}$ days.
So either II or III are sufficient for answering the problem.