In the following question, select the missing number from the given response.

Two people A and B are at a distance of 110 km from each other at 10:30 AM. After 30 minutes, A starts moving towards B at a speed of 20 km/hr while at 12 PM. B starts moving away from A at a speed of 15 km/hr. At what time (in AM) will they meet on the next day?

Let A and B meet at point C after t hours from 11 a.m. AB = 110 km. ⇒ AC – BC = 110 km. ⇒ 20t – 15 (t – 1) = 110 ⇒ 20t – 15t + 15 = 110 ⇒ 5t = 110 – 15 = 95 $Rightarrow t=frac{95}{5}=19$ hours ∴ Required time = 19 hours after 11 am. = at 6 am next day Alternative:

A has stopped for $frac{1}{2}$ an hour

∴ Distance travelled by A in 1 hour

= Speed × Time

= 20 × 1 = 20 km

Reamining distance = 110 – 20 = 90 km

Relative speed = 20 – 15 = 5 kmph

Time taken to cover the remaining distance

$=frac{ ext { Remaining distance }}{ ext { Relative speed }}=frac{90}{5}=18$ hours

∴ Meeting time of A and B = 12 PM + 18 hours

= 6:00 A.M.