Ashakti invested the same amount of money in two distinct Systematic Investment Plans (SIPs), SIP 'X' and SIP 'Y,' both for a duration of 2 years. SIP 'X' yields simple interest at a rate of 'R%' per annum, and SIP 'Y' provides compound interest (compounded annually) at the same interest rate as SIP 'X'. If the ratio of the interest earned on SIP 'X' to that on SIP 'Y' is 100:109, determine the value of 'R'.

ATQ, Let, the interest received on SIP 'X' and SIP 'Y' be Rs.'100x' and Rs.'109x', respectively. In case of simple interest, equal interest is received in each year at same rate of interest. So, the simple interest received on first and second year both = (100x/2) = Rs.'50x' At same rate of interest, Simple interest received in first year = Compound interest received in first year = (100x/2) = Rs.'50x' So, the compound interest received on second year = 109x - 50x = Rs.'59x' So, the interest in second year received on interest received on first year at 'R%' p.a.,= 59x - 50x = Rs.'9x' So, the rate of interest, 'R' = (9x/50x) × 100 = 18%