In scheme A and B, Rs. ‘z’ and Rs. ‘(z+5000)’ were invested at the rate of (R-6)% and ‘R’% per annum on simple interest. After two years, the ratio between the interest obtained from scheme A and B is 91:128 respectively. If Rs. 45000 was invested on compound interest at the rate of (R-2)% per annum compounded annually, then Rs. 31050 was obtained as an interest after 2 years. The value of ‘z’ is what percentage of the value of ‘R’?

Solution

If Rs. 45000 was invested on compound interest at the rate of (R-2)% per annum compounded annually, then Rs. 31050 was obtained as an interest after 2 years. 45000 of (100+(R-2))% of (100+(R-2))% = 31050+45000 4.5x(100+(R-2))x(100+(R-2)) = 76050 (100+(R-2))x(100+(R-2)) = 16900 R²+196R−7296=0 R²+(228-32)R−7296=0 R²+228R-32R−7296=0 R(R+228)-32(R+228)=0 (R+228) (R-32) = 0 R = -228, 32 The value of ‘R’ cannot be negative. So R = 32 . In scheme A and B, Rs. ‘z’ and Rs. ‘(z+5000)’ were invested at the rate of (R-6)% and ‘R’% per annum on simple interest. After two years, the ratio between the interest obtained from scheme A and B is 91:128 respectively. (z x (R-6) x 2)/100 : ((z+5000) x R x 2)/100 = 91:128 (z x (R-6) x 2) : ((z+5000) x R x 2) = 91:128 Put the value of ‘R’ in the above equation. (z x (32-6) x 2) : ((z+5000) x 32 x 2) = 91:128 (z x 26 x 2) : ((z+5000) x 32 x 2) = 91:128 (z) : (z+5000) = 7 : 8 8z = 7z+35000 z = 35000 Required percentage = (35000/32)x100 = 109375%