 Hello and welcome to the session. Let's work out the following problem. It says a train travels a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km an hour, the journey would have taken 2 hours less. Find the original speed of the train. So let's now move on to the solution. We have to find the original speed of the train. So let the original speed be equal to x km per hour. And we are given that train travels a distance of 300 km. Now let T1 be the time taken to cover a distance of 300 km with the speed x km per hour. Now the time taken is given by the formula distance upon speed must write this formula. So T1 is given by the distance which is 300 km and speed which is x km per hour. Now when the speed is increased by 5 km per hour, therefore increased speed would be x plus 5 km per hour since original speed is x km per hour. And now the speed is increased by 5 km per hour. So now the increased speed is x plus 5 km per hour. So now the time taken with increased speed let it be T2. It is 300 upon x plus 5 hours since the distance travelled is 300 km and now the speed is x plus 5 km per hour. Now we are given that when the speed is increased the journey would have taken 2 hours less. That means when the speed was x km per hour then the time taken by the train was 2 hours more than the time taken by the train when the speed is x plus 5 km per hour. So to equate these 2 times we need to subtract 2 hours from this time. So according to question we have 300 upon x minus 2 is equal to 300 upon x plus 5. Now this implies 300 upon x minus 300 upon x plus 5 is equal to 2. So taking 300 common and taking LCM in the numerator will have x plus 5 minus x upon LCM would be x into x plus 5 is equal to 2. Now plus x gets cancelled with minus x and we have 300 into 5 is equal to 2 into x into x plus 5. Now taking 2 common on both sides or dividing both sides by 2 we have dividing 300 by 2 we have 150 into 5 is equal to dividing 2 by 2 is 1. So we have x into x plus 5 which is x square plus 5x. So this implies x square plus 5x minus 150 into 5 is 750 it is equal to 0. Now we will factorize this quadratic equation so we have x square plus 30x minus 25x minus 750 is equal to 0. Now this implies taking x common from the first 2 terms we have x into x plus 30 taking minus 25 common from the last 2 terms we have minus 25 into x plus 30 is equal to 0. Now taking x plus 30 common we have x plus 30 into x minus 25 is equal to 0. So this implies x plus 30 is equal to 0 or x minus 25 is equal to 0 and this implies x is equal to minus 30 or x is equal to 25. But since x is the speed of the train it cannot be negative so this is rejected as speed cannot be negative. Therefore x is equal to 25 hence original speed of the train is equal to 25 kilometer per hour. So this completes the question and the session. Bye for now. Take care. Have a good day.