A train P going at the speed of 70 km/h completely passes train Q of length 170 m. going in the same direction on parallel tracks at 56 km/h in $$1\frac{1}{2}$$​   minutes, How much time (in seconds) will P take to cross completely train R of length 220m. going at 74 km/h in the opposite direction?

Correct option is C

Given:

Speed of train P = 70km/hr

Speed of train Q = 56km/hr

Length of train Q = 170m

Time taken by train P to pass train Q = $$1\frac{1}{2}minutes$$​​

Formula Used:

Distance =$$Speed \times Time$$​​

Solution:

Let the length of train P be x

Relative Speed of train when going in same direction = (70 - 56 ) = 14km/hr

Speed in metre per second = $$14 \times \frac{5}{18} = \frac{35}{9}m/sec$$​​

Time taken =$$1\frac{1}{2} =\frac{3}{2}minutes \times 60 = 90 \ seconds$$​​

Total distance covered by train P while crossing $$= \frac{35}{9}\times 90 = 350\ metres$$​​

Length of train P = 350 - 170 = 180m

Now length of train R is 220m and speed of train R= 74km/hr

Relative speed when both the train are in opposite direction = 74 + 70 = 144km/hr

Speed in metre per second = $$144 \times \frac{5}{18}$$​= 40m/sec

Total distance to be covered = 220 + 180 = 400m

Time taken $$= \frac{400}{40}$$​= 10 seconds