 Hello and welcome to the session. In this session we discuss the following question which says the difference between the compound interest and the simple interest on a certain sum for two years at 6% per annum is rupees 30, find the sum. Let's recall the formula for the simple interest that is s i is equal to p r t upon 100 where this p is the principal, r is the weight of interest and t is the time. Then the formula for the compound interest t i is equal to amount that is a minus the principal p amount is given by the formula p into 1 plus r upon 100 whole to the power n minus p. Here we have p is the principal, r is the weight of interest and n is the time. This is the key idea to be used for this question. Now we proceed with the solution. We need to find out the sum so we assume let the sum be equal to rupees 100 that is we have taken the principal p equal to rupees 100. We are given the rate of interest r equal to 6% per annum and the time t is equal to 2 years or you can say this is equal to n also. Since we use n in the formula for the amount which is to be used for the formula for compound interest. Now first we find the simple interest s i this would be equal to rupees putting the values for p r and t in this formula. So we get this is equal to rupees 100 into 6 into 2 upon 100. This would be equal to rupees 12 is the simple interest. Now we calculate the compound interest by putting the values for p r and n in the formula given in the key idea. So this would be equal to rupees p that is 100 into 1 plus r upon 100 that is 6 upon 100 whole to the power 2 minus rupees 100 that is the value for p. This is further equal to rupees 100 into 106 upon 100 into 106 upon 100 minus rupees 100. Now this 100 and this 100 gets cancelled and this would be equal to rupees 112.36 minus rupees 100 and so we have compound interest c i is equal to rupees 12.36. Now we have the simple interest as rupees 12 and the compound interest as rupees 12.36. Now the compound interest c i minus the simple interest s i is equal to rupees 12.36 minus rupees 12 and this is equal to rupees 0.36 is the difference between the compound interest and the simple interest. Now if the difference between compound interest and the simple interest is rupees 0.36 then the sum is rupees 100. Now in the question we have the difference between compound interest and simple interest as rupees 30. So if we have the difference between the compound interest and the simple interest is rupees 30 then the sum would be equal to rupees 100 upon 0.36 into 30 and this comes out to be equal to rupees 8333.33. So if given the difference between compound interest and simple interest as rupees 30 we would get the sum as rupees 8333.33. Hence our final answer is rupees 8333.33. So this completes the session hope you have understood the solution for this question.