A train travels 360 km at a uniform speed If the speed

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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:

Let the actual speed of train = ‘x’  km/h

So, time taken by the train at actual speed = \frac{360}{x} hr

Increased speed of the train = (x + 5) km/h

So, time taken by the train at the increased speed =\frac{360}{(x + 5)} hr

According to the given condition

\Rightarrow \dfrac{360}{x} - \dfrac{360}{(x + 5)} = 1

\Rightarrow \dfrac{360[x + 5 - x]}{x(x + 5)} = 1

⇒ 360×5 = x(x + 5)

⇒   x² + 5x – 1800 = 0

⇒  x² + 45x  – 40x – 1800 = 0

⇒   x(x + 45) – 40(x + 45) = 0

⇒    (x + 45)(x – 40) = 0

⇒  x = 40, -45[ not possible as speedd can not be negative]

Hence, the actual speed of the 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 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: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 :For solution please click here

 

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