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1. The true discount on a certain of money due $2 \frac{2}{3}$ years hence, is Rs. 150 and the simple interest on the same sum for the same time and at the same rate is Rs. 200. Interest rate per annum is ?

A. 10%

B. 12%

C. $12 \frac{1}{2} %$

D. $8 \frac{1}{2} %$

Solution:

\begin{aligned} True Discount = Rs . 150 \\ and \\ Simple interest = Rs . 200 \\ Sum due = \frac{S .I . \times TD}{(S .I .) - (TD)} \\ = Rs . (\frac{200 \times 150}{200 - 150}) \\ = Rs . 600 \\ ∴ Rate \\ = (\frac{100 \times 200}{600 \times \frac{8}{3}}) % \\ = (\frac{20000}{1600}) % \\ = (\frac{200}{16}) % \\ = 12 \frac{1}{2} % \end{aligned}

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