The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs. 100 and Rs. 80 respectively. What is the sum and the time?
A. Sum = Rs. 400 and Time = 5 years
B. Sum = Rs. 200 and Time = 2.5 years
C. Sum = Rs. 400 and Time = 2.5 years
D. Sum = Rs. 200 and Time = 5 years
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & BD = {\text{Rs}}.100 \cr & TD = {\text{Rs}}{\text{.}}\,80 \cr & R = 10\% \cr & F{\text{ = }}\frac{{BD \times TD}}{{(BD - TD)}} \cr & \,\,\,\,\,\,\, = \frac{{100 \times 80}}{{(100 - 80)}} \cr & \,\,\,\,\,\,\, = \frac{{100 \times 80}}{{20}} \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,400 \cr} $$BD = Simple Interest on the face value of the bill for unexpired time = $$\frac{{FTR}}{{100}}$$
$$\eqalign{ & \Rightarrow 100 = \frac{{400 \times T \times 10}}{{100}} \cr & \Rightarrow 100 = 4 \times T \times 10 \cr & \Rightarrow 10 = 4 \times T \cr & \Rightarrow T = \frac{{10}}{4} = 2.5{\text{years}} \cr} $$
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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