Correct option is (A) 8
Let the amount taken be Rs P.
\(\therefore\) S.I. = \(\frac{16}{25}\times\) P = \(\frac{16P}{25}\)
R = T
\(\therefore\) S.I. = \(\frac{PRT}{100}\)
\(\Rightarrow\) \(\frac{16P}{25}\) = \(\frac{P\times R\times R}{100}\) \((\because\) R = T)
\(\Rightarrow\) \(R^2=\) \(\frac{16P}{25}\times\frac{100}P\) \(=16\times4=64=8^2\)
\(\Rightarrow\) R = 8
\(\Rightarrow\) T = R = 8
Correct option is (C) ₹ 2166.66
Let the amount be P.
R = \(12\frac{1}{2}\%=\frac{25}{2}\%\)
T = 1 year
Amount after 1 year \(=P(1+\frac R{100})^1\)
\(\Rightarrow\) \(P(1+\frac R{100})\) = 2437.50 (Given)
\(\Rightarrow\) \(P(1+\frac{25}{200})\) = 2437.50
\(\Rightarrow\) \(P(1+\frac18)\) = 2437.50
\(\Rightarrow\) \(\frac{9P}8\) = 2437.50
\(\Rightarrow\) P = 2437.50 \(\times\frac89=\frac{19500}9\) = 2166.66
\(\therefore\) Amount is Rs 2166.66