 Hello and welcome to the session. The given question says, the speed of a boat in still water is 11 km per hour. It can go 12 km up the stream and return down the stream to the original point in 2 hours and 45 minutes. Find the speed of the stream. Let's start with a solution and let the speed of the stream is equal to x km per hour. We are given that speed of a boat in still water is equal to 11 km per hour. Therefore, this implies speed down the stream is speed of the boat in still water plus the speed of the stream that is 11 plus x km per hour and up the stream is equal to 11 minus x km per hour. Now, we know that the formula to calculate the time is equal to distance divided by speed. Therefore, according to the equation, first it traveled 12 km up the stream. So, we have distance 12 divided by the speed to travel up the stream is 11 minus x. Then, it came back to the original point down the stream. So, we have plus 12 divided by 11 plus x and the total time taken to go up the stream and come down the stream is 2 hours and 45 minutes. We have 12 divided by 11 minus x plus 12 divided by 11 plus x is equal to 2 and 45 minutes is equal to 3 divided by 4 hours. So, we have 2 then 3 by 4. Right? Now, it is simplified further. We have 12 divided by 11 minus x plus 12 divided by 11 plus x is equal to 11 by 4 or we have taking Lcm on the left hand side we have 11 minus x into 11 plus x and the numerator we have 12 times of 11 plus x plus 12 times of 11 minus x and this is equal to 11 divided by 4 or we have 12 into 11 is equal to 132 plus 12x plus 132 minus 12x divided by 11 square minus x square is equal to 11 by 4 or we have 132 plus 132 is 264 12x cancels out of minus 12x and we have in the denominator 121 minus x square is equal to 11 divided by 4 on cross multiplying we have 11 into 121 minus x square is equal to 4 into 264 or we have 11 into 121 gives 1331 minus 11x square is equal to on multiplying 4 by 264 we get 1056 plus us further equal to 11x square is equal to 1331 minus 1056 or we have 11x square is equal to 175 or x square is equal to 275 divided by 11 which is equal to 25 or x is equal to plus minus 5 now since x is the speed of the stream and the speed cannot be negative therefore x is equal to minus 5 is rejected and therefore x is equal to 5 kilometers per hour hence the answer is speed of the stream is equal to 5 kilometers per hour so this completes the session by intake