Symbiosis National Aptitude Test SNAP 2019 Paper

Let Rohan and, Rahul meets at point C, any where between point A and B. They meets after t hours.
Distance covered by Rohan in t hours = 8t km
Distance covered by Rahul in 1st hours = (3 + 1) km
Distance covered by Rahul in 2nd hours = (3 + 2) km
Distance covered by Rahul in 3rd hours = (3 + 3) km
Distance covered by Rahul in 4th hours = (3 + t) km
Total distance covered by Rahul
= (3 + 1) + (3 + 2) + (3 + 3) + ... + (3 + t)
= $\left\{3\mathit{t}+\frac{\mathit{t}\left(\mathit{t}+1\right)}{2}\right\}$ km
Sum of distance travelled by Rohan and Rahul = 144
8t + 3t + $\frac{\mathit{t}\left(\mathit{t}+1\right)}{2}$ = 144
${\mathit{t}}^2$ + 23t = 288
⇒ ${\mathit{t}}^2$ – 23t – 288 = 0
(t + 32)(t – 9) = 0
⇒ t = 9, –32
∴ t = 9 hour
[neglecting the negative sign]
Now, Distance travelled by Rohan in 9 hours = 8 × 9 = 72 km
∴ Distance AC = 72 km
Hence, Rohan and Rahul will meet at midway of A and B