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 %.