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1. The banker's discount on a sum of money for $1 \frac{1}{2}$ years is Rs. 120. The true discount on the same sum for 2 years is Rs. 150. What is the rate per cent?

A. $3 \frac{1}{3} %$

B. $4 \frac{1}{3} %$

C. $3 \frac{2}{3} %$

D. $4 \frac{2}{3} %$

Solution:

\begin{aligned} B D for 1 \frac{1}{2} years = Rs . 120 \\ B D for 2 years = 120 \times \frac{2}{3} \times 2 \\ = Rs . 160 \\ T D for 2 year = R s . 150 \\ F = \frac{B D \times T D}{(B D - T D)} \\ = \frac{160 \times 150}{160 - 150} \\ = \frac{160 \times 150}{10} \\ = Rs . 2400 \end{aligned}

⇒ Rs.160 is the simple interest on Rs. 2400 for 2 years

\begin{aligned} \Rightarrow 160 = \frac{2400 \times 2 \times R}{100} \\ \Rightarrow R = \frac{160 \times 100}{2400 \times 2} \\ = \frac{160}{48} \\ = \frac{20}{6} \\ = \frac{10}{3} \\ = 3 \frac{1}{3} % \end{aligned}

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