 Hello and welcome to the session. In this session we discussed the following question which says Taxi charges in a city consist of fixed charges per day and the remaining depending upon the distance traveled in kilometers. If a person travels 100 kilometers he pays Rs 700 and for driving 200 kilometers he pays Rs 1200. Find the fixed charges per day and the rate per kilometer. So in this question we need to find the fixed charges per day and the rate per kilometer according to the conditions given and the conditions given are that if a person travels 100 kilometers he would pay Rs 700 and if he travels 200 kilometers he would pay Rs 1200. Now let's see the solution. So first of all we assume that the fixed charges per day be equal to Rs X per day then we also assume that the rate per kilometer be equal to Rs Y per kilometers and we need to find the values for these X and Y. Now when a person travels 100 kilometers he pays Rs 700 so when the person travels 100 kilometers then the fixed charges would be added that is X plus 100 into Y that is he travels 100 kilometers and rate per kilometer is Rs Y so for 1 kilometer since the person pays Rs Y for 100 kilometers he would pay Rs 100 Y so the fixed charges plus the charges for traveling that is X plus 100 Y and this is equal to total Rs 700. So we have got one equation that this be equation 1. Then in the equation we are given that when a person travels 100 kilometers he pays Rs 1200 so the equation for this would be given by adding the fixed charges that is X plus the charges for traveling which would be 200 into Y since for 1 kilometer he pays Rs Y so for 200 kilometers he would pay Rs 200 Y and X plus 200 Y would be equal to 1200 since he pays Rs 1200 for traveling Rs 200 kilometers. So this is equation 2. So we get 2 equations X plus 100 Y is equal to 700 this is equation 1 and X plus 200 Y equal to 1200 this is equation 2. Now we will solve both these equations for the values for X and Y. To solve these 2 equations we subtract equation 1 from equation 2 and we get X plus 200 Y minus X plus 100 Y is equal to 1200 minus 700 this gives us X plus 200 Y minus X minus 100 Y is equal to 500 or you can say we get 100 Y is equal to 500 from here we have Y is equal to 500 upon 100 which is equal to 5 thus we get Y is equal to 5 now we will get the value of X by substituting Y equal to 5 in equation 1 this gives us X plus 100 into Y that is X plus 100 into 5 is equal to 700 that is we have X plus 500 is equal to 700 from here we get X is equal to 700 minus 500 that is equal to 200 so the value of X plus obtained is 200 and we had assumed X to be the fixed charges per day and Y to be the rate per kilometer thus we say fixed charges per day is given by rupees 200 per day then rate per kilometer is equal to rupees 5 per kilometer so this is our final answer this completes the session hope you have understood the solution for this question