An amount of Rs. (y-2800) was invested on simple interest at the rate of (R+1)% per annum for 6 years. An another amount of Rs. (y+3200) was invested on simple interest at the rate of (R-2)% per annum for 5 years. The interest obtained in both of the cases is the same. Which of the following are the possible values of ‘y’ and ‘R’?

(i) 14800, 12

(ii) 15800, 16

(iii) 14800, 14

(iv) 12800, 18

Solution

An amount of Rs. (y-2800) was invested on simple interest at the rate of (R+1)% per annum for 6 years. Interest after 6 years = (y-2800)x(R+1)%x6    Eq.(i) An another amount of Rs. (y+3200) was invested on simple interest at the rate of (R-2)% per annum for 5 years. Interest after 5 years = (y+3200)x(R-2)%x5    Eq.(ii) The interest obtained in both of the cases is the same. So Eq.(i) = Eq.(ii) (y-2800)x(R+1)%x6 = (y+3200)x(R-2)%x5 (i) 14800, 12 (14800-2800)x(12+1)%x6 = (14800+3200)x(12-2)%x5 12000x13%x6 = 18000x10%x5 9360 ≠ 9000 So these are not the correct values.  (ii) 15800, 16 (15800-2800)x(16+1)%x6 = (15800+3200)x(16-2)%x5 13000x17%x6 = 19000x14%x5 13260 ≠ 13300 So these are not the correct values.  (iii) 14800, 14 (14800-2800)x(14+1)%x6 = (14800+3200)x(14-2)%x5 12000x15%x6 = 18000x12%x5 10800 = 10800 So these are the correct values.  (iv) 12800, 18 (12800-2800)x(18+1)%x6 = (12800+3200)x(18-2)%x5 10000x19%x6 = 16000x16%x5 11400 = 12800 So these are not the correct values.