The banker's discounted on a sum of money for 1 ¹/ ₂ years is Rs. 60 and the true discount on the same sum for 2 years is Rs. 75. The rate percent is?

B.D. = Rs. (5840 - 5767.20) = Rs. 72.80
Rs. 72.80 is S.I. on Rs. 5840 at 7%
So, Unexpired time = (100 x 72.80) / (7 x 5840) = 13/73 years = 65 days.
Now, date of draw o bill = April, 4 at 6 months.
Nominally due date = October 4.
Legally due date = October 7
So, we must go back 65 days from October 7.
Oct., sept., Aug. = 7 + 30 + 28
i.e., The bill was discounted on 3rd August.

Let the amount of bill be Rs. 100
Money deducted = Rs. 4
Money receive by holder of the bill = Rs. (100 - 4) = Rs. 96
S.I. on Rs. 96 for 10 months = Rs. 4
Rate = [(100 x 4 x 6) / (96 x 5)] = 5%

S.I. on Rs. 1600 is P.W. of Rs. 1624
i.e. Rs. 24 is the S.I. on Rs. 1600 at 6%
? Time = (100 x 24) / (1600 x 6) = 1/4 year = 3 months

Sum = (B.D. x T.D.) / (B.D - T.D.) = (52 x 50) / 2 = Rs. 1300
Since B.D. is S.I. on sum due, so S.I. on Rs. 1300 for 8 months is Rs. 52 consequently.
Rate = [(100 x 52)] / [1300 x (2/3)] % = 6%

P.W. = Rs. (540 - 90) = Rs. 450
S.I. on Rs. 450 = Rs. 90
B.D. = S.I. on Rs. 540
= Rs. (90/450) x 540 = Rs. 108

Give that A = ? 13800 , R = 5%
T = 5 yr and BG = ?
According to the formula,
BG = [A(R x T)²] / [100(100 + R x T)]
= [13800(5 x 5)²] / [100(100 + 5 x 5)]
= (13800 x 625) / (100 x 125)
= ? 690

Given that, R = 24%, T = 24 months= 2 yr and TD = ? 144
BD = TD + BG
According to the formula,
BG = (TD x R x T)/100 = (144 x 24 x 2)/100
= ? 69.12
? BD = 144 + 69.12 = ? 213.12

Given that, PW = ? 2200, TD = ? 220
According to the formula,
BG = (TD)²/PW = (220 x 220)/2200 = ? 22
BD = (TD + BG) = ?(220 + 22) = ? 242

Given that PW = ? 576 , BG = ? 9 and TD = ?
TD = PW x BG
= 576 x 9
= 24 x 3
= ? 72

Given that, n = 81
According to the formula.
R = 10?1/n%
= 10?1/81%
= 10 x (1/9) % = 1¹/_{9 %}