If the difference between CI and SI on a certain sum at

If the difference between CI and SI on a certain sum at r% per annum for 2 years is ₹ x, find the expression for principal sum. If the difference between CI and SI on a certain sum at 4% per annum for 2 years is ₹ 25, find the sum.

Let the sum be ₹ P

SI =	Pr × 2	=	2 Pr
	100		100

C.I. = P			1 +	r		²	− 1
				100

= P		1 +	r²	+	2r	− 1
			(100)²		100

CI = P		r²	+	2r
		100²		100

CI – SI = P		r²	+	2r		−	2Pr
		100²		100			100

Let, CI – SI = y

y =	Pr²	⇒ P = y		100		₂
	100²			r

Here, y = ₹ 25 , r = 4% per annum

P = 25		100		²
		4

P = 25× 625
P = ₹ 15625.