 Hello and welcome to the session. Let us understand the following questions today. A train covered a certain distance at a uniform speed. If the train would have been 10 km per hour faster, it would have taken 2 hours less than the scheduled time and if train was slower by 10 km per hour it would have taken 3 hours more than the scheduled time. Finally distance covered by the train. Now let us first understand how we take out the speed. Speed is equal to distance upon time and this is the formula which we will be using in the question. So this is our key idea. Now let us write the solution. Let the actual speed of train be equal to x km per hour and let the actual time taken is equal to y hours. So distance covered is equal to speed into time from key idea. So it is equal to xy. Now according to question if speed is increased by 10 km per hour then speed is equal to x plus 10 km per hour. In this case time taken is reduced by 2 hours which is equal to y minus 2 hours. Therefore distance covered is equal to speed multiplied by time which is equal to x plus 10 multiplied by y minus 2 and which is equal to xy which we have found here. So now solving this we get which implies xy is equal to xy minus 2x plus 10y minus 20 which implies distance gets cancelled. So we are left with 2x minus 10y plus 20 is equal to 0. Taking two common from this equation we get it implies x minus 5y is equal to minus 10. This is our first equation. Now taking the other case when speed is reduced by 10 km per hour then speed is equal to x minus 10 km per hour. And in this case time taken is increased by 3 hours which is equal to y plus 3 hours. Therefore distance covered is equal to speed multiplied by time which implies distance covered is xy which is equal to x minus 10 multiplied by y plus 3. Now solving this we get this implies xy is equal to xy plus 3x minus 10y minus 30 which implies distance gets cancelled. So we are left with 3x minus 10y is equal to 30. This is our equation 2. Now solving equation 1 and 2 we have x minus 5y plus 10 is equal to 0 and 3x minus 10y minus 30 is equal to 0 are the equations 1 and 2. Now solving this solving equation 1 and 2 multiplying equation 1 by 2 we get 2x minus 10y is equal to minus 20 and writing equation 2 as it is that is 3x minus 10y is equal to 30. Now subtracting do not forget to change the signs while subtracting. So we see that distance gets cancelled and 2x minus 3x is equal to minus x which is equal to minus 20 minus 30 is equal to minus 50. Now this minus and minus gets cancelled and this implies x is equal to 50. Now substituting x is equal to 50 in equation 1 we get equation 1 is x minus 5y plus 10 is equal to 0 x minus 5y plus 10 is equal to 0 now x is equal to 50 minus 5y plus 10 is equal to 0 which implies minus 5y is equal to minus 60 this minus and minus gets cancelled which implies y is equal to 60 divided by 5 which gets cancelled by 12 which implies y is equal to 12. Now we see that x is equal to 50 which we have earlier assumed to be speed which we have earlier assumed to be speed and y is time so this is equal to speed and y is equal to 12 which is equal to time. So distance is equal to xy where x is speed and y is the time which is equal to 50 multiplied by 12 which is equal to 600 kilometer hence we require distance is equal to 600 kilometer I hope you understood the problem bye and have a nice day.