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?
Answer & explanation
Correct answer: option 3
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
.PNG)
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