QUESTION

# A passenger train takes one hour less for a journey of 150km if its speed is increased by 5km/hr from its usual speed. The usual speed of the train is …………… km/hr.

Hint- For solving such types of questions we need to let the speed of the vehicle and form an equation and then find the value of the quantity.

Time taken to cover the journey with usual speed=$\dfrac{{{\text{distance}}}}{{speed}}$=$\dfrac{{150}}{x}$ hr
Therefore, time taken to complete the journey=$\dfrac{{{\text{distance}}}}{{speed}}$= $\dfrac{{150}}{{x + 5}}$ hr
$\dfrac{{150}}{x} - \dfrac{{150}}{{x + 5}} = 1 \\ 150(\dfrac{1}{x} - \dfrac{1}{{x + 5}}) = 1 \\ 150(\dfrac{{(x + 5) - (x)}}{{x.(x + 5)}}) = 1 \\ 150(\dfrac{5}{{x.(x + 5)}}) = 1 \\ 150 \times 5 = x.(x + 5) \\ {x^2} + 5x - 750 = 0 \\ {x^2} + 30x - 25x - 750 = 0 \\ x(x + 30) - 25(x + 30) = 0 \\ (x - 25)(x + 30) = 0 \\ x = 25, - 30 \\$