 Hello and welcome to the session. In this session we discuss the following question which says if three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 6 as the remainder. Also if seven times the smaller number is divided by the larger number, we get 4 as quotient and 22 as remainder. Find the numbers. So in this question we have two numbers, a larger number and a smaller number and we are given some conditions. So let's try to find out these numbers. First of all we assume that the larger number be equal to x and we assume the smaller number to be equal to y. We know that dividend is equal to divisor into quotient plus remainder. Now first of all one condition in the question given to us is that three times the larger number is divided by the smaller number. So this means when three times the larger number that is 3x is divided by the smaller number that is y then we get quotient as 4 and remainder as, so therefore using this well that is dividend is equal to divisor into quotient plus remainder we get dividend that is 3x is equal to divisor that is y into quotient that is 4 plus remainder that is 6 which gives us 3x is equal to 4y plus 6 or you can say we get 3x minus 4y is equal to 6. This is our equation 1. Next we are given in the question that seven times the smaller number is divided by the larger number. So when seven times the smaller number and smaller number is y so 7y is divided by the larger number which is x then we get quotient equal to 4 and remainder equal to 22. Therefore again we get dividend that is 7y is equal to divisor which is x multiplied by the quotient that is 4 plus the remainder that is 22. So this gives us 7y is equal to 4x plus 22 or we get minus 4x plus 7y is equal to 22. Let this be equation 2. So now we get two equations 3x minus 4y equal to 6 this is equation 1 and minus 4x plus 7y is equal to 22 this is equation 2. Now let's solve equations 1 and 2 to get the values for x and y. So for this we multiply equation 1 by minus 4 so multiplying equation 1 by minus 4 we get minus 4 into 3x minus 4y equal to 6. So this gives us minus 12x plus 16y is equal to minus 24. We take this as equation 3. Next we will multiply equation 2 by 3 and this would give us 3 multiplied by minus 4x plus 7y equal to 22 that is we get minus 12x plus 21y is equal to 66. We take this as equation 4. Now the two equations that we get is minus 12x plus 16y equal to minus 24 and minus 12x plus 21y is equal to 66. This is equation 3 and this is equation 4. Now we shall subtract equation 3 from equation 4 and this would give us minus 12x plus 21y minus minus 12x plus 16y is equal to 66 minus 24. From here we have minus 12x plus 21y plus 12x minus 16y is equal to 66 plus 24. Now 12x and minus 12x cancels. Now 21y minus 16y gives us 5y and this is equal to 90 that is y is equal to 90 upon 5 and 18 5 times is 90. Therefore we get y is equal to 18. Now substituting y equal to 18 in equation 1 we get 3x minus 4y that is 4 into 18 is equal to 6. This gives us 3x minus 72 is equal to 6 which further gives us 3x is equal to 78 and from here we get x is equal to 78 upon 3 and 26 3 times is 78. Thus x is equal to 26 and as you know that we had assumed that the larger number be x and the smaller number be y. So we have got the larger number equal to x equal to 26 and the smaller number equal to y is equal to 18. So thus the required numbers are 26 and 18 out of which 26 is the larger number and 18 is the smaller number. So this completes the session. Hope you have understood the solution for this question.