SSC CGL Tier II 12 Jan 2017 Paper 1

(2)A’s speed = x kmph.
B’s speed = y kmph.
When A and B move in opposite directions they meet at C and when they move in the same direction, they meet at D.
Case I,
AC + CB = AB
$\frac{\mathit{x}}{2}+\frac{\mathit{y}}{2}=15$
$\Rightarrow \mathit{x}+\mathit{y}=30.....\left(\mathit{i}\right)$
Case II,
AD – BD = AB
⇒ $\mathit{x}\times \frac{5}{2}\mathit{–}\mathit{y}\times \frac{5}{2}=15$
$\frac{5}{2}\left(\mathit{x}\mathit{–}\mathit{y}\right)=15$
$\Rightarrow \mathit{x}-\mathit{y}=\frac{15\times 2}{5}=6.....\left(\mathit{i}\mathit{i}\right)$
∴ On adding equations (i) and (ii),
x + y + x – y = 30 + 6
⇒ 2x = 36
⇒ x = $\frac{36}{2}$ = 18 kmph.