P starts from A at 6 a.m. and reaches B after 8 hours. A starts from B at 8 a.m. and reaches A after 9 hours. When they meet, what is the ratio of the distance travelled by Q to the distance travelled by P?

6 : 11

Time taken by P from A to B = 8 hours

Time taken by Q from B to A = 9 hours

Let us consider that , Distance between point A to B is = 72 km

Speed of P = \(\frac{72}{8}\) = 9

Speed of Q = \(\frac{72}{9}\) = 8

Distance covered by P till 8 am = 9 × 2 = 18 km

So, AC = 18 km

Distance covered by P in next 6 hours = 9 × 6 = 54 km

⇒ BC = 54 km

Time taken  by them to meet at M = \(\frac{54}{9 + 8}\) 

= \(\frac{54}{17}\) hours

Distance BM = 8 × \(\frac{54}{17}\) = \(\frac{432}{17}\) km 

Distance CM = 9 × \(\frac{54}{17}\) = \(\frac{486}{17}\) km

We know that ,

AM = AC + CM

= 18 + \(\frac{486}{17}\)

= \(\frac{792}{17}\) km

Now,

BM  :  AM

\(\frac{432}{17}\)  :  \(\frac{792}{17}\)

6  :  11