A train covers a distance of 480 km at a uniform speed

by

Question 4:

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, it would have taken 3 hours more to cover the same distance. Find the original speed of the train.                [CBSE    2020]

Solution:

Let the original speed of the train  = x km/h.

Time of journey of 480 km = \frac{480}{x} hours

Time taken to cover a journey of 480 km with speed of (x – 8) km/h = \frac{480}{(x-8)} hours

Now according to the question.

\frac{480}{(x-8)} - \frac{480}{x} = 3

\Rightarrow 480\left[\frac{x - (x-8)}{x(x-8)}\right] = 3

\Rightarrow 480\left[\frac{x - x + 8}{x(x-8)}\right] = 3

\Rightarrow 480\left[\frac{ 8}{x(x-8)}\right] = 3

\Rightarrow 3x(x - 8) = 3840

\Rightarrow x(x - 8) = 1280

\Rightarrow x^2 - 8x = 1280

\Rightarrow x^2 -8x - 1280 = 0

\Rightarrow x^2 - 40x + 32 x - 1280 = 0

⇒ x(x – 40) + 32(x – 40) = 0$

⇒  (x – 40)(x + 32) = 0

⇒ x = 40,  -32(Not possible)

Thus the original speed of train is = 40 km/h.

Question:1

If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her present age. What is her present age ?                   [CBSE Term-2 SQP 2022]

Solution: For solution please  click here

Question 2:

The sum of areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.                     [CBSE 2019]

Solution:  For solution please  click here

Question 3:

If the equation (1 + m²)x² + 2 mcx + c² – a² = 0 has equal roots then show that c² = a²(1 + m²).

[CBSE 2017]

Solution: For solution please click here

Question 5:

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200km/hr and time of flight increased by 30 minutes. Find the original duration of flight .      [CBSE  2020]

Solution :

Question 6:

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hours less for the same journey. Find the speed of the train.                                                                                   [CBSE  2019]

Solution: For solution please click here

Leave a Comment