The simple interest and compound interest (compounded annually) on a certain sum of money with a given rate for a period of 2 years are Rs.900 and Rs.954 respectively. The sum of money is
Options:
A . Rs.3750
B . Rs.3700
C . Rs.3850
D . Rs.3650
Answer: Option A Answer: (a)Difference of CI and SI for two years= Rs.(954 - 900) = Rs.54Sum= Difference in CI and SI × $(100/{Rate})^2$Rate = ${2 × \text"Difference" × 100}/\text"Simple interest"$= ${2 × 5400}/900 = 12%$Sum = 54 × $(100/12)^2$= $54 × 25/3 × 25/3$ = Rs.3750Using Rule 10,C.I. = Rs.954, S.I.=Rs.900, P=?C.I.= S.I.$(1 + R/200)$954 = 900$(1 + R/200)$$954/900 = 1 + R/200$$954/900 - 1 = R/200$${954 - 900}/900 = R/200$$54/9 = R/2$R = 12%Now S.I. = ${P × R × T}/100$900 = ${P × 12 × 2}/100$P = Rs.3750
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