Management Aptitude Test 2017 Paper

(d) 28 hours
Let, 'd' be the total distance between A and B and
let 'M' be the meeting point.
Then, A covers V distance and B covers (d - x ) distance, before meeting

Also, $\frac{\mathrm{Speed}\mathrm{of}\mathrm{car}1}{\mathrm{Speed}\mathrm{of}\mathrm{car}2}$ = $\sqrt{\frac{16}{9}}=\frac{4}{3}$
Let, us assume that the speed of car 1 and car 2 is 4y and 3y, respectively.
∴ $\frac{\mathit{x}}{4\mathit{y}}=\frac{\mathit{d}-\mathit{x}}{3\mathit{y}}$
⇒ $\frac{\mathit{x}}{4}=\frac{\mathit{d}-\mathit{x}}{3}$
⇒ 3x = 4d - 4x
⇒ 7x = 4d
⇒ x = $\frac{4\mathit{d}}{7}$
Now, it is given that car 2 covers $\frac{4\mathit{d}}{7}$ distance in 16 hours.
∴ $\frac{\frac{4\mathit{d}}{7}}{16}$ = 3y
⇒ $\frac{4\mathit{d}}{7\times 16}$ = 3y
⇒ $\frac{\mathit{d}}{3\mathit{y}}=\frac{7\times 16}{4}$ = 28 hours