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