The bankers discount and the true discount of a sum at 10% per annum simple inte

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Question
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?
Options
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

Correct Answer

Sum = Rs.400 and Time = 2.5 years

Explanation

BD = Rs.100

TD = Rs.80

R = 10%

$F = \frac{B D � T D}{B D - T D} = \frac{100 � 80}{100 - 80} = R s . 400$

BD = Simple interest on the face value of the bill for unexpired time= FTR/100

$? 100 = \frac{400 � T � 10}{100}$

=> T = 2.5 years