NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 Question 2 (iv)

NCERT Class X Chapter 4: Quadratic Equation Exercise 4.1 2 (iv)

Question:

Represent the following situations in the form of quadratic equations :A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Given:

Distance traveled = 480 km

If speed was 8 km/h less, time taken would be 3 hours more.

To Find:

Quadratic equation representing the situation to find the speed of the train.

Formula:

WKT, Time = Distance / Speed.

Solution:

Let the uniform speed of the train (in km/h) = x
Time taken to cover 480 km at uniform speed (t1 in hours) = 480 x
If the speed had been 8 km/h less, the new speed (in km/h) = (x - 8)
Time taken to cover 480 km at reduced speed (t2 in hours) = 480 x - 8
According to the problem, t2 = t1 + 3.

⇒ 480 x - 8 = 480 x + 3
To eliminate denominators, multiply the entire equation by x(x - 8):

⇒ 480x = 480(x - 8) + 3x(x - 8)

⇒ 480x = 480x - 3840 + 3x2 - 24x
Move all terms to one side to set the equation to 0:

⇒ 0 = 3x2 - 24x - 3840
Divide the entire equation by 3 to simplify (optional, but good practice):

⇒ x2 - 8x - 1280 = 0

Result:

The situation can be represented by the quadratic equation:

x2 - 8x - 1280 = 0.
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