 Hello and welcome to the session. In this session we discussed the following question which says divide Rs. 3700 into two parts so that the simple interest on the first part for 8 months at 10% per annum is equal to the simple interest on the second part for 1.5 years at 12% per annum. Before moving on to the solution let's recall the formula. For the simple interest si is equal to p into r into t upon 100 where this p is the principal r is the rate of interest per annum, t is the time in years. This is the key idea to be used in this question. Let's proceed with the solution now. We take let the first part be equal to Rs. x now that we are given that Rs. 3700 is divided into two parts and we have taken the first part to be x so the second part would be equal to Rs. 3700-x. Now let's consider the first part we will find the simple interest on the first part. Here we are given the principal that is p is Rs. x then the rate of interest is 10% per annum that is we have the rate of interest r is equal to 10% per annum then time t is equal to 8 months which is equal to 8 upon 12 years. Now simple interest si is equal to p into r into t upon 100 so simple interest si is equal to Rs. x into 10 into 8 upon 12 upon 100 that is we have substituted the values for p, r and t in the formula for si so we get this would be equal to Rs. x into 10 into 8 upon 100 into 12 now 0 cancels with the 0 then 4 2 times is 8 and 4 3 times is 12 so this is equal to Rs. 2x upon 30 or we also have that 2 15 times is 13 so this is equal to Rs. x upon 15 is the si or the simple interest on the first part. Now let's consider the second part and find out the simple interest on the second part. Now the principal p for the second part is Rs. 3700-x then the rate of interest r on the second part I have given in the question is 12% per annum so here we have for the second part r would be equal to 12% per annum then the time t is given as 1.5 years so time t for the second part is equal to 1.5 years or you can say this is equal to 3 upon 2 years. Now simple interest si is equal to Rs. principal that is 3700-x into r that is 12 into time that is 3 upon 2 upon 100 so this is equal to Rs. 3700-x into 12 into 3 upon 100 into 2 now 2 6 times is 12 and 2 3 times is 6 and 2 50 times is 100 so we get this is equal to Rs. 9 into 3700-x upon 50 this is the simple interest si on the second part and in the question is given that the simple interest on the first part is equal to the simple interest on the second part so we have according to the question simple interest on the first part which is Rs. x upon 15 that is x upon 15 is equal to the simple interest on the second part that is 9 into 3700-x upon 50 so this gives us x upon 15 is equal to 33300-9x upon 50 now cross multiplying we get 50x is equal to 15 into 33300-9x that is we have 50x is equal to 49950-135x so we get 50x plus 135x is equal to 49950 this gives us 185x is equal to 49950 so from here we get x is equal to 49950 upon 185 now solving this we have 185 2700 times is 49950 so we get x is equal to 2700 that we have the first part is equal to Rs. 2700 since we had assumed the first part to be x and the second part is equal to Rs. 3700-x so this is equal to Rs. 3700-2700 equal to Rs. 1000 thus first part is equal to Rs. 2700 and second part is equal to Rs. 1000 this completes the session hope you have understood the solution for this question