 Hi and welcome to the session. My name is Shashi and I am going to help you with the following question. Question is, form the pair of linear equations for the following problems and find their solution by substitution method. Fourth part is, the taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 kilometer, the charge paid is Rs 105 and for a journey of 15 kilometer, the charge paid is Rs 155. What are the fixed charges and the charge per kilometer? How much does a person have to pay for traveling a distance of 25 kilometers? Reading the question carefully, you can see that two quantities are unknown that is the fixed charges and the charge per kilometer. Now for solution, let the fixed charge is equal to rupees x and let the charge for 1 kilometer is equal to rupees y. Now we are having the condition that for a distance of 10 kilometer, the charge paid is rupees 105. So we can say that according to the question, charge paid for 10 kilometer plus fixed charges is equal to rupees 105. We know that fixed charges are to be added for all distances. Now we know that charge for 1 kilometer is equal to rupees y. So the charge paid for 10 kilometer would be 10 y equal to rupees x. So therefore we get the first equation as 10 y plus x is equal to 105. Now another condition given in the question is for a journey of 15 kilometer, the charge paid is rupees 155. So this implies kilometers plus fixed charges must be equal to rupees 155. Therefore our second equation is 15155. We can see that the charge for 1 kilometer is equal to rupees y. So the charges for 15 kilometer would be 15 y. So the charges are added for all distances. So our second equation is 15 y plus x is equal to 155. These equations as equation 1 and equation 2. From equation 1, we get minus 10 y. Equation as substituting the value of x, equation 2 we get 25 minus 105. We can say, so therefore our y is equal to substitute the value of y is equal to 10 in the equation 3 to get the value of x. Substituting the value of y is equal to 10 in equation 3, we get x is equal to 105 minus 10 multiplied by, this implies x is equal to 105 minus 100. Therefore x is equal to charge is equal to rupees 2, rupees 5 and the charge for 1 kilometer is equal to rupees y is equal to rupees 10. The last part asked in the question is how much does a person have to pay for traveling a distance of 25 kilometers. Now the payment rate for traveling a distance of 25 kilometer is equal to charge for 25 kilometer plus fixed charge. You know charge for 25 kilometer would be 25 multiplied by 10 and the fixed charge is equal to rupees 5. So we get required payment is equal to 25 multiplied by 10 plus rupees 5 which is equal to 250 plus 5 which is further equal to rupees 255. So the required equations are 10y plus x is equal to 105, 15y plus x is equal to 155. Fixed charges that is rupees x is equal to rupees 5 kilometer that is rupees y is equal to rupees 10 and the payments for traveling a distance of already 5 kilometer is equal to rupees 255. This is our final answer. Hope you understood this session. Have a nice day and goodbye.