A sum of money at simple interest amounts to 1,012 in 212years

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A sum of money at simple interest amounts to 1,012 in 2 1
2
years and to 1,067.20 in 4 years. The rate of interest per annum is :

According to question ,

Principal + S.I. for	5	yrs = ₹ 1012.............(i)
	2

Principal + S.I. for 4 years = 1067.20 ...(ii)
Subtracting equation (i) from (ii)

S.I. for	3	yrs = ₹ 55.20
	2

∴ S.I. for	5	yrs	= 55.20 ×	2	×	5	= ₹ 92
	2			3		2

∴ Principal = Amount - SI = (1012 – 92) = ₹920

Rate =	2 × 92 × 100	= 4%
	920 × 5

Second method to solve this question :
Here , A₂ = ₹ 1067.20 , T₁ = 5 /2 years , A₁ = ₹ 1012 , T₂ = 4 years

R =		A₁ - A₂		× 100
		A₂T₁ - A₁T₂

R =		1012 - 1067.20		× 100
		1067.20 ×(5 ÷2) - 1012 × 4

R =	- 55.2	× 100
	(2668 - 4048)

R =	- 55.2	× 100
	- 1380

R = 4%