Which of the following can be true?

i. R reached the destination in 5hrs and P reached the destination in 3 hrs

ii. R reached the destination is 3 hrs and P reached the destination in 5 hrs

iii. If the distance is increased by 90 km and the speed of P is 1/5th of the speed of Q, then R reached the new distance at 3.30 pm

Solution

Speed of Q = √625 m/sec = 25 m/sec = 25 x 18/5 = 90 km/hr Time taken to reach point B by Q = 8 hrs (11.30 am – 7:30 pm) Distance between A and B = 90 x 8 = 720 km Speed of P = 0.8 x 90 = 72 km/hr Now, From i: We know that speed of R is more than that of P. Hence time taken by R will be less than that of P. So, statement I is false. From ii: Time taken by Q to reach at point B is 8 hrs but, in the statement, it is written that R will reach the destination in 3 hrs, which is not possible as speed of R is more than that of Q. Hence, statement ii is false. From iii: If distance is increased by 90 km, then new distance = 720 + 90 = 810 km Speed of P = 1/5 x 90 = 18 km/hr Time taken by P = 810/18 = 45 hrs Now distance is increased, then time to reach the destination by P will also increase. And it is also given that the person who is fastest will reach by 7:30 pm. So, R will not cover the new distance by 3:30 pm. Hence statement iii is also false.