(b) 8%
Let the sum be Rs P and rate of interest per annum be R%
Then, P\(\Big[\big(1+\frac{R}{100}\big)^2-1\Big]\) - \(\frac{2PR}{100}\)
= Rs 832 – Rs 800 = Rs 32
\(\Rightarrow\) P\(\Big[1+\frac{2R}{100}+\frac{R^2}{10000}-1\Big]\) - \(\frac{2PR}{100}\) = 32
\(\Rightarrow\) \(\frac{PR^2}{10000}\) = 32 \(\Rightarrow\) PR x R = 320000.......(i)
Also, \(\frac{2PR}{100}\) = 800 (S.I) \(\Rightarrow\) PR = 40000 ..........(ii)
\(\therefore\) From (i) and (ii)
40000 × R = 320000 \(\Rightarrow\) R = 8% p.a