# A sum of money amounts to 5200 Rs. in 5 years and to 5680 Rs. in 7 years at simple interest. The rate of interest per annum is :

A sum of money amounts to 5200 Rs. in 5 years and to 5680 Rs. in 7 years at simple interest. The rate of interest per annum is :

[A]3%

[B]4%

[C]5%

[D]6%

**6%**

P + SI 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 years = 240

∴ From equation (I),

P + 5 $latex \times$ 240 = 5200

$latex => P = 5200 – 1200 = 4000 Rs.$

$latex \therefore R = \frac{SI\times 100}{T\times P}&s=1$

$latex = \frac{240\times 100}{1\times 4000} = 6\%&s=1$

Hence option [D] is correct answer.