A train takes 2 hours less for a journey of 300 km by increasing its speed by 5 km/h. What is its normal speed?

Correct option is B

Given:

Distance of journey = 300 km

Time difference = 2 hours

Increased speed = Normal speed + 5 km/h

Formula Used:

Time = Distance / Speed

Solution:

Let the normal speed be x km/h.

Time taken at normal speed = 300 / x

Time taken at increased speed = 300 / (x + 5)

According to the problem:

​$$\frac{300}{x} - \frac{300}{x + 5} = 2$$​​

Simplifying the equation:

​$$\frac{300(x + 5) - 300x}{x(x + 5)} = 2\\\ \\\frac{1500}{x(x + 5)} = 2$$​​

1500 = 2x(x + 5)

1500 = 2x² + 10x

2x² + 10x - 1500 = 0

Solving the quadratic equation:

x² + 5x - 750 = 0

Using the quadratic formula:

​$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$​​

Here, a = 1, b = 5, and c = -750

​$$x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-750)}}{2(1)}$$

​$$x = \frac{-5 \pm \sqrt{25 + 3000}}{2}\\\ \\x = \frac{-5 \pm \sqrt{3025}}{2}\\\ \\x = \frac{-5 \pm 55}{2}$$​​

Taking the positive root:

​$$x = \frac{-5 + 55}{2}$$​​

x = 25

The normal speed is 25 km/h.

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