NTSE Stage 2 MAT 2014 Question Paper

Let a & b be the speed of boat and the speed of the current
From statement I
According to statement I
a = b + 2
a – b = 2 ...(i)
From statement II
b = a + 1
b – a = 1 ...(ii)
Compare statement (i) & (ii), we get the speed of the boat is not possible.
From statement III
$\mathit{x}=\frac{\mathit{y}}{\left(\mathit{a}+\mathit{b}\right)}+\frac{\mathit{y}}{\left(\mathit{a}-\mathit{b}\right)}$
$\frac{\mathit{x}}{\mathit{y}}=\frac{2\mathit{a}}{\left(\mathit{a}+\mathit{b}\right)}\left(\mathit{a}-\mathit{b}\right)$ ...(iii)
Compare equation (i) & (iii), we get
$\frac{\mathit{x}}{\mathit{y}}=\frac{2\mathit{a}}{\left(2\mathit{a}-2\right).2}$
$2\mathit{a}\mathit{x}-2\mathit{x}=\mathit{a}\mathit{y}$
∴ $\mathit{a}=\frac{2\mathit{x}}{2\mathit{x}-\mathit{y}}$
So the speed of boat $=\frac{2\mathit{x}}{2\mathit{x}-\mathit{y}}$
Thus statement I & III together are sufficient for answering the problem.