 Hello and welcome to the session. Let us discuss the following question. It says, a plane left 30 minutes later, then there's a new time, and in order to reach its destination 1,500 kilometer away in time, it has to increase its speed by 250 kilometer per hour from its usual speed, find its usual speed. So let's now proceed on with the solution. Let the usual speed, kilometer per distance travel minutes later than its scheduled time, in order to reach its destination, which is 1,500 kilometer away, it increases the speed by 250 kilometer per hour. So the distance, 1,500 kilometer. Now the time taken when speed is kilometer per 1,500 kilometer, and the speed is x kilometer per hour. So the time taken is 1,500 upon x kilometer pleased by 250 kilometer per hour from its usual speed. So the speed is time taken would be 1,500 upon the speed, which is x plus 250 kilometer per hour. Since we are given that the plane left half an hour later, then it's scheduled time. The speed x to 1,500 upon x minus half an hour is equal to 1,500 upon x plus 250 LCM. Here we have LCM as 2x, and we multiply 2 with 1,500. So we have 3,000 minus x is equal to 1,500 upon x plus 250. Now cross multiplying, we have x plus 250 into 3,000 minus x is equal to 1,500 into 2x is 3,000 x. Now multiplying the two brackets, we have x into 3,000 is 3,000 x. x into minus x is minus x squared. 250 into 3,000 is 7,500,000. Plus 250 into minus x is minus 250 x is equal to 3,000 x. Now 3,000 x gets answered on both sides. And we have the quadratic equation minus x squared minus 250x plus 7,500,000. Now taking negative side common, we have equation as x squared plus 250x,500,000 is equal to 0. Now we'll solve this quadratic equation for x. So we have x squared plus 1,000 x,000,000 is equal to 0. Now taking x common from the first two terms, we have x into x plus 1,000. And taking minus 750 common from the last two terms, we have minus 750 into x plus 1,000 is equal to 0. Now taking x plus 1,000 common, we have x plus 1,000 into x minus 750 is equal to 0. Now this implies either x plus 1,000 is equal to 0 or x minus 750 is equal to 0. And this implies x is equal to minus 1,000 or x is equal to 750. Now we have assumed that x is the speed of the plane and speed cannot be negative. So we'll reject x is equal to minus 1,000. Therefore, the usual speed kilometer per question and the session by for now take care, have a good day.