A man borrowed some money from a private organisation at

A man borrowed some money from a private organisation at 5% simple interest per annum. He lended 50% of this money to another person at 10% compound interest per annum and thereby the man made a profit of Rs. 3,205 in 4 years. The man borrowed.

Suppose Sum borrowed = Rs. P
Given that , Rate ( R ) = 5% , Time = 4 years

∴ Simple interest after 4 years ( SI ) =	P × 4 × 5	= Rs.	P
	100		5

Amount lent of on compound interest = Rs.	x
	2

∴ C.I. = P			1 +	R		^T	− 1
				100

C.I. =	P			1 +	10		⁴	− 1
	2				100

C.I. =	P	[(1.1)⁴ − 1]
	2

C.I. =	P	(1.4641 − 1)
	2

C.I. = Rs.	0.4641P
	2

∴ C.I. - S.I. = 3205

∴	0.4641P	−	P	= 3205
	2		5

⇒	2.3205P − 2P	= 3205
	10

⇒ 0.3205P = 32050

⇒ P =	32050	= Rs. 100000
	0.3205