The simple interest and compound interest (compounded annually)

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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 ₹ 900 and ₹ 954 respectively. The sum of money is

1. ₹ 3700
2. ₹ 3650
3. ₹ 3850
4. ₹ 3750

Correct Option: D

Here , CI for two years = ₹ 954 and SI for two years = ₹ 900
As per the given in question ,
Difference of CI and SI for two years = ₹ (954 – 900) = ₹ 54

Rate =	2 × Difference × 100
	Simple interest

Rate =	2 × 54 × 100	= 12%
	900

∴ Sum = Difference in CI and SI ×		100		²
		Rate

⇒ Sum = 54 ×		100		²
		12

Sum = 54 ×	25	×	25	= ₹ 3750
	3		3

Second Method to solve this question :
C.I. = Rs. 954 , S.I.= Rs. 900 , P = ?

C.I.= S.I.		1 +	R
			200

954 = 900		1 +	R
			200

954	= 1 +	R
900	= 1 +	200

954	− 1 =	R
900	− 1 =	200

954 − 900	=	R
900	=	200

54	=	R
9	=	2

∴ R = 6 × 2 = 12%

Now S.I. =	P × R × T
	100

900 =	P × 12 × 2	⇒ P = Rs. 3750
	100