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1. The true discount on a certain sum due 6 months hence at 15% is Rs. 240. What is the banker's discount on the same sum for the same time at the same rate?

A. Rs. 258

B. Rs. 278

C. Rs. 228

D. None of these

Solution:

\begin{aligned} T D = Rs . 240 \\ T = 6 months = \frac{1}{2} year \\ R = 15 % \\ T D = \frac{B G \times 100}{T R} \\ \Rightarrow 240 = \frac{B G \times 100}{(\frac{1}{2} \times 15)} \\ B G = \frac{240 \times 15}{100 \times 2} \\ = \frac{120 \times 15}{100} \\ = Rs . 18 \\ B G = B D - T D \\ \Rightarrow 18 = B D - 240 \\ \Rightarrow B D = 18 + 240 \\ = Rs . 258 \end{aligned}

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