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. $$4\frac{2}{3}\,\% $$
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & BD{\text{ for }}1\frac{1}{2}{\text{ years}} = {\text{Rs}}{\text{.}}\,\,120 \cr & BD{\text{ for }}2{\text{ years}} = 120 \times \frac{2}{3} \times 2 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,160 \cr & TD\,{\text{for}}\,2\,{\text{year}} = Rs.\,150 \cr & F = \frac{{BD \times TD}}{{\left( {BD - TD} \right)}} \cr & \,\,\,\,\,\,\,\, = \frac{{160 \times 150}}{{160 - 150}} \cr & \,\,\,\,\,\,\,\, = \frac{{160 \times 150}}{{10}} \cr & \,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,2400 \cr} $$⇒ Rs.160 is the simple interest on Rs. 2400 for 2 years
$$\eqalign{ & \Rightarrow 160 = \frac{{2400 \times 2 \times R}}{{100}} \cr & \Rightarrow R = \frac{{160 \times 100}}{{2400 \times 2}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{160}}{{48}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{6} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{10}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3\frac{1}{3}\,\% \cr} $$
Related Questions on Bankers Discount
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
A. Rs. 400
B. Rs. 360
C. Rs. 480
D. Rs. 320
A. 3 months
B. 4 months
C. 6 months
D. 8 months
A. Rs. 480
B. Rs. 520
C. Rs. 600
D. Rs. 960
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