[Sum = Rs.400 and Time = 2...] The bankers discount and the true discount of a sum at 10% per annum simple interest for the same ti

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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?

Sum = Rs.400 and Time = 5 years

Sum = Rs.200 and Time = 2.5 years

Sum = Rs.400 and Time = 2.5 years

Sum = Rs.200 and Time = 5 years

Explanation:

BD = Rs.100

TD = Rs.80

R = 10%

F = $\dfrac{BD \times TD}{BD-TD}$

$= \dfrac{100 \times 80}{(100-80)} = \dfrac{100 \times 80}{20} =Rs.400$

BD = Simple Interest on the face value of the bill for unexpired time $=\dfrac{FTR}{100}$

$\Rightarrow 100 = \dfrac{400 \times \text{T} \times 10}{100}$

$\Rightarrow 100 = 4 \times {T} \times 10$

$\Rightarrow 10 = 4 \times {T}$

$\Rightarrow {T} $= $\dfrac{10}{4} $= 2.5 years

Additional Questions

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