The banker’s gain on a certain sum due 5/2 years hence is 9/25 of the banker’s discount. What is the rate percent?
Answer: D
T = 5/2 year
Let the banker’s discount, BD = Rs.1
Then, banker’s gain, BG = (9/25)*1 = Rs. 9/25
BG = BD-TD
=> 9/25 = 1-TD
=> TD = 1-9/25 = 16/25
F = BD*TD/(BD-TD)
= (1*16/25)/(1-(16/25)) (16/25)/(9/25) = Rs. 16/9
BD = simple interest on the face value of the bill for unexpired time = FTR/100
=> 1 = (16/9)*(5/2)*R/100
=> 100 = (16/9)*(5/2)*R
=> 100 = 16*5*R/9*2
=> 100 = 8*5*R/9
=> R = 100*9/8*5
= 100*9/40 = 5*9/2 = 45/2 = 22 1/2 %