Test: Speed, Time & Distance - 2 - UPSC MCQ

Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr

Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4

So distance traveled on foot = 4(4) = 16 km

Let the distance be x
Let the original speed be y
Time originally taken = distance / speed
That means = x/y
Now the new speed is (6/7)y
And new time is distance /new speed
x/(6/7)y that can be written as 7x/6y
Now new time - original time = 12 min
7x/6y-x/y=12
After subtracting we get
x/y = 12×6
x/y = 72min

If the distance between house and office is d km
Then time taken to go from home to office = d/3 hr (Time = Distance/Speed)
and Time taken to come back from office to home= d/2 hr
So total time taken = (d/3 +d/2) hour
But according to question , time taken = 5 hour
so we have
d/3+d/2=5
or (2d+3d)/6= 5
or 5d/6=5
or, d=5 x6/5= 6km
So distance between home and office = 6km

Total Distance = 10 +12 = 22 km
Total time = 10/12 + 12/10 = 5/6 + 6/5 = 25/30 + 36/30 = 61/30 hours
Average speed = 22 /(61/30) = 660/61 = 10.8 km/ hour

Let the speed of the car be x km/h

So the speed of the train will be 1.5x km/h

According to the question

⇒ 75/x - 75/1.5x = 12.5/60

⇒ (112.5 - 75)/1.5x = 12.5/60

⇒ 37.5/1.5x = 12.5/60

⇒ 1.5x = 37.5 × (60/12.5)

⇒ x = 180/1.5

⇒ x = 120 km/h

∴ The speed of the car is 120 km/h

option "D"

Distance he could travelled/speed diff.
= 20/(14-10)
= 20/4
= 5 hrs
Now his actual speed was 10 km/h
Total distance travelled by him = speed × time
= 10 × 5
= 50 km.
 

Given 

The ratio of speed of two trains = 7 : 8 

Formula Used 

Distance = speed × time

Calculation 

Let the speed of trains be 7x and 8x respectively

Speed of 2nd train = 400/4 = 100 km/hr 

According to the question 

⇒ 8x = 100 

⇒ x = 12.5km/hr

So, speed of 1st train = 7x = 7 × 12.5 = 87.5 km/hr 

∴ The speed of 1st train is 87.5 km/hr

Eight hours for a 600 km journey, when 120 km is done by train and 480 km by car.

It takes 20 minutes more if 200 km is done by train and 400 km by car.

Formula used:

Speed = Distance/Time

Calculation:

Let the speed of the train be x km/h

And the speed of the car be y km/h

⇒ 120/x + 480/y = 8

⇒ 120(1/x + 4/y) = 8

⇒ 1/x + 4/y = 1/15     ...i)

In the second condition

⇒ Total time = 8 + 20/60 = 25/3 hr

∴  200/x + 400/y = 25/3

⇒ 200(1/x + 2/y) = 25/3

⇒ 1/x + 2/y = 1/24     ...ii)

After solving equation (i) and (ii)

(By substracting equation 2 from equation 1)

⇒ x = 60 km/h

⇒ y = 80 km/h

Ratio of the speed of train and car is

⇒ 60 : 80

⇒ 3 : 4

∴ The ratio of the speed of train and car is 3 : 4.

Let the speed of the train be x km/hr and that of the car be y km/hr.
It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car.
120/x + 480/y = 8 or 1/x + 4/y = 1/15
If 200 km is done by train and the rest by car, then 20 minutes more time is taken.
200/x + 400/y = 25/3 or 1/x + 2/y  = 1/24
Solving both the equations,
x = 60 and y = 80
Ratio is 3 : 4