Raju took some amount from a bank at 10\(\frac{1}{2}\) % per 1 year. He paid ₹ 1863.75 as interest after 2\(\frac{1}{2}\) years. Then how much amount was initially taken ?
A) ₹ 6,500
B) ₹ 1,600
C) ₹ 6,800
D) ₹ 7,100
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Correct option is (D) ₹ 7,100
Let initially taken amount = Rs P.
Time = \(2\frac{1}{2}\) years = \(\frac52\) years
Rate = \(10\frac{1}{2}\%\) = \(\frac{21}{2}\%\)
S.I. = 1863.75
\(\because\) S.I. = \(\frac{P\times R\times T}{100}\)
\(\Rightarrow\) \(\frac{P\times\frac{21}2\times\frac52}{100}\) = 1863.75
\(\Rightarrow\) \(P=\frac{1863.75\times100\times4}{21\times5}\) = 7100
\(\therefore\) Initially taken amount of Raju = Rs 7100.
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