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1. The banker's discount on a sum of money for $1 \frac{1}{2}$ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

A. 10%

B. 13%

C. 12%

D. 15%

Solution:

\begin{aligned} B .D . for \frac{3}{2} years = R s . 558 \\ B .D . for 2 years \\ = R s . (558 \times \frac{2}{3} \times 2) \\ = R s . 744 \\ T .D . for 2 years = R s . 600 \\ ∴ Sum = \frac{B . D . \times T . D .}{B . D . - T . D .} \\ = R s . (\frac{744 \times 600}{144}) \\ = R s . 3100 \\ Thus, Rs . 744 is S .I . on Rs . 3100 for 2 years . \\ ∴ Rate = (\frac{100 \times 744}{3100 \times 2}) % \\ = 12 % \end{aligned}

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