A man invests half his capital at the rate of 10% per annum,

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A man invests half his capital at the rate of 10% per annum, onethird at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets, is

Let the principal be p .
We know that ,

∴ SI =	P × R × T
	100

∴ SI₁ =	p × 10 × 1	=	p
	2 × 100		20

SI₂ =	p × 9 × 1	=	3p
	3 × 100		20

SI₃ =	p	×	12 × 1	=	p
	6		100		50

∴ SI₁ + SI₂ + SI₃ =		p	+	3p	+	p
		20		100		50

SI₁ + SI₂ + SI₃ =		5p + 3p + 2p		=	p
		100			10

∴ Average annual rate = 10%