​ The banker’s gain on a bill is 1/9th of the banker’s discount, rate of interest being 10% p.a. ​

Question

The banker’s gain on a bill is \(\frac{1}{9}\)th of the banker’s discount, rate of interest being 10% p.a. Find the unexpired period of the bill.

Answer 1

Given BG = \(\frac{1}{9}\)BD & r = 0.1

9(BD – TD) = BD 

8BD = 9TD 

BD . 8BD = 9 . \(\frac{BD}{1 + trr}\)

1+ tr = \(\frac{9}{8}\) = 1.125 

tr = 1.125 – 1 t(0.1) = 0.125 

t = \(\frac{0.125}{0.1}\) = 1.25 years 

t = 1.25 × 12 = 15 months