A sum of money amounts to 5,200 in 5 years and to 5,680

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A sum of money amounts to 5,200 in 5 years and to 5,680 in 7 years at simple interest. The rate of interest per annum is

1. 3%
2. 4%
3. 5%
4. 6%

Correct Option: D

According to question ,
P + S.I. for 5 years = 5200 ..(i)
P + SI for 7 years = 5680 ...(ii)
On subtracting equation (i) from (ii),
SI for 2 years = 480
∴ SI for 1 year = ₹ 240
∴ From equation (i),
⇒ P + 5 × 240 = ₹5200
⇒ P = 5200 – 1200 = ₹ 4000

∴ R =	S.I × 100
	T × P

R =	240 × 100	= 6%
	1 × 4000

Second method to solve this question :
Here , A₂ = ₹ 5680 , T₁ = 5 years , A₁ = ₹ 5200 , T₂ = 7 years

R =		A₁ - A₂		× 100
		A₂T₁ - A₁T₂

R =		5200 - 5680		× 100
		5680 × 5 - 5200 × 7

R =	- 480	× 100
	28400 - 36400

=	- 480	× 100
	- 8000

R = 6%