 Hello and welcome to the session. In this session we discuss the following question which says, the speed of a boat in still water is 15 km per hour. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream. So we are given the speed of the boat in still water. And the distance that it covers upstream and downstream is 30 km and the total time taken is 4 hours 30 minutes. So we have to find the speed of the stream. Let's see the solution now. First of all we assume that the speed of the stream is equal to x km per hour. Now speed of the boat in still water is given as 15 km per hour. Then the speed downstream would be equal to 15 plus x that is speed of the boat in still water plus the speed of the stream that is 15 plus x km per hour. And then the speed upstream would be equal to the speed of the boat in still water that is 15 minus the speed of the stream that is x. So 15 minus x km per hour is the speed upstream. So it's given that the distance traveled upstream is equal to 30 km. So now time taken by the boat to go 30 km upstream would be equal to the distance which is 30 upon the speed upstream which is 15 minus x hours. I think the question is given that it goes 30 km upstream and also returns downstream to the original point. So downstream also the distance traveled would be equal to 30 km. So we have time taken by the boat to go 30 km downstream is equal to the distance which is 30 upon the speed downstream which is 15 plus x. So 30 upon 15 plus x hours is the time taken by the boat to go 30 km downstream. In the question we are given that the total time taken by the boat to return to the original point is 4 hours 30 minutes which means this is equal to minus upon 2 hours. So we can now say that the time taken by the boat to go 30 km upstream which is 30 upon 15 minus x plus the time taken by the boat to go 30 km downstream which is 30 upon 15 plus x is equal to the total time taken by the boat to return to the original point which is minus upon 2 hours. Now let's try solving this. So taking LCM on the left hand side we get 15 minus x this whole into 15 plus x in the denominator. In the numerator we have 30 multiplied by 15 plus x plus 30 multiplied by 15 minus x this is equal to minus upon 2. This further gives us 450 plus 30x plus 450 minus 30x upon 225 plus 15x minus 15x minus x square is equal to minus upon 2. Now 30x and minus 30x cancels and in the denominator 15x and minus 15x cancels this gives us 900 upon 225 minus x square is equal to 9 upon 2. Now cross multiplying gives us 1800 is equal to 225 minus x square this whole into 9 that is further we have 1800 is equal to 2025 minus 9x square from here we get 9x square is equal to 2025 minus 1800. This further gives us 9x square is equal to 225 that is x square is equal to 225 upon 9. Now 925 times is 225 so we have x square is equal to 25 which gives us x equal to plus minus 5 and we had assumed x to be the speed of the stream. So we have but the speed of the stream cannot be negative therefore x is not equal to minus 5 and so we have x is equal to 5. Thus we say the speed of the stream is equal to 5 kilometers per hour so 5 kilometers per hour is our final answer. This completes the session hope you have understood the solution of this question.