The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?

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Solution

Simple Interest on Rs. 1600 = True Discount on Rs.1680.
Rs. 1600 is the Present Worth (PW) of Rs. 1680
Rs. 80 is the Simple Interest of Rs.1600 at $15 % \Rightarrow 80 = 1600 \times T \times \frac{15}{100}$
$\Rightarrow 80 = 16 \times T \times 15$
$\Rightarrow 5 = T \times 15$
$\Rightarrow 1 = T \times 3$
$\Rightarrow T = \frac{1}{3}$
year $= \frac{12}{3} m o n t h s = 4 m o n t h s$

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The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?

Simple Interest on Rs. 1600 = True Discount on Rs.1680. Rs. 1600 is the Present Worth (PW) of Rs. 1680 Rs. 80 is the Simple Interest of Rs.1600 at 15%⇒80=1600×T×15100 ⇒80=16×T×15 ⇒5=T×15 ⇒1=T×3 ⇒T=13 year =123 months=4 months