Unitary Method Test - 3

Let the speed of man is u and that of current is v

Downstream speed will be u + v

Upstream speed will be u − v

He travels 20 km downstream in 4 hrs

So, downstream speed is 20/4 = 5 km/hr

Similarly, upstream speed will be 12/4 = 3 km/hr

So, u + v = 5

⇒ u – v = 3
Subtracting both the equations;

⇒ 2v = 2

⇒ v = 1 km/hr

Train was halted for half an hour.

So, total time taken in Journey = 25 - (1/2) = 24.5 hours.

Average speed in Whole Journey = 1000/24.5 = 48.9 km/hr.

The average speed on return journey is 30% less than onward journey.

Therefore, ratio of average speed of onward and return journey,

= 100/70 = 10/7.

Let average speed of onward journey = 10x.

Average speed on return journey = 7x.

Average speed on whole journey = (10x +7x)/2

48.9 = (10x + 7x)/2

97.8 = 17x

x = 5.75.

Average speed on return = 7x = 7 × 5.75 = 40.25 km/h

= 40 km/h (approx.)

Distance travelled by car in 3hrs=81km

So, speed of the car = 84/2 = 42 km

Distance travelled by car in 4 hrs = 42 × 4 = 168 km

Given a person travels 75 km in 5 hrs in a car.

Then speed of the car is distance/time = 75/5 = 15 km/ hr