a) ₹ 670 & 8%

b) ₹ 675 & 8.5%

c) ₹ 675 & 8%

d) ₹ 660 & 8%

correct answer is: c) ₹ 675 & 8%

**Explanation**

Here, A sum of money means ‘Principal’ .

In 2 years, amount is ₹ 783 .

In 3 years, amount is ₹ 837 .

So that, 1 year Simple interest is =₹\left(837\;-\;783\right)

\rightarrow\ ₹ 54

So, in 2 years,

Simple interest is = ₹\left(54\times2\right)

\rightarrow\ ₹ 108

and Principal is =\left(Amount\ -\ S.I\right)

\rightarrow₹\left(783-108\right)

\rightarrow\ ₹ 675

We know, Rate =\frac{100\times S I}{P\times T}

\therefore Rate =\frac{100\times108}{675\times2}

\rightarrow\ 8 % p.a.**Ans:** The sum is ₹ 675 & per annum rate 8 %.