On certain amount simple interest is \(\frac{16}{25}\)th part of the a

1.	On certain amount simple interest is \(\frac{16}{25}\)th part of the amount taken then the time and rate of interest is ……………….. (Numerically same) A) 8 B) 9 C) 10 D) 3
Answer» 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 A) 8

On certain amount simple interest is \(\frac{16}{25}\)th part of the amount taken then the time and rate of interest is ……………….. (Numerically same) A) 8 B) 9 C) 10 D) 3

Answer»

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 A) 8