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1. The banker's gain on a certain sum due $1 \frac{1}{2}$ years hence is $\frac{3}{25}$ of the banker's discount. The rate percent is:

A. $5 \frac{1}{5}$ %

B. $9 \frac{1}{9}$ %

C. $8 \frac{1}{8}$ %

D. $6 \frac{1}{6}$ %

Solution:

\begin{aligned} Let, B .D . = Rs . 1 \\ Then, B .G . = Re . \frac{3}{25} \\ ∴ T .D .  = (B .D .  -  B .G .) \\ = Rs . (1 - \frac{3}{25}) \\ = Rs . \frac{22}{25} \\ Sum = \frac{1 \times \frac{22}{25}}{1 - \frac{22}{25}} \\ = Rs . \frac{22}{3} \\ S .I . on Rs . \frac{22}{3} for 1 \frac{1}{2} years is Rs . 1 \\ ∴ Rate = (\frac{100 \times 1}{\frac{22}{3} \times \frac{3}{2}}) % \\ = 9 \frac{1}{9} % \end{aligned}

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