Aptitude Bankers Discount Practice QA

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

F = Rs.5840

R = 7%

BD = 5840 - 5767.20 = Rs.72.8

=>72.8 = $\dfrac{5840 \times T \times 7}{100}$

=>T = $\dfrac{72.8 \times 100}{7 \times 5840} $= $\dfrac{10.4 \times 100}{5840}$

=$\dfrac{1040}{5840}$ = $\dfrac{104}{584}$= $\dfrac{13}{73}$ years

=$ \dfrac{13 \times 365}{73}$days= 65days

=> Unexpired Time = 65 days

Given that Date of Draw of the bill = 4^th April at 6 months

=> Nominally Due Date = 4^th October

=> Legally Due Date = [4^thOctober + 3 days] = 7^th October

Hence, The date on which the bill was discounted

= [7^th October - 65 days]

= [7^th October - 7 days in October - 30 days in September - 28 days in August]

= 3^rd August

F = Rs. 3000

R = 10%

Date on which the bill is drawn = 14th July at 5 months

Nominally Due Date = 14th December

Legally Due Date = 14th December + 3 days = 17th December

Date on which the bill is discounted = 5th October

Unexpired Time

= [6th to 31st of October] + [30 Days in November] + [1st to 17th of December]

= 26 + 30 + 17 = 73 Days

$= \dfrac{73}{365}$year = $\dfrac{1}{5}$year

BD = Simple Interest on the face value of the bill for unexpired time

$= \dfrac{FTR}{100} = \dfrac{ 3000 \times \dfrac{1}{5} \times 10}{100}$

$= 30 \times \dfrac{1}{5} \times 10$= Rs.60

TD = Rs. 240
T = 6 months = $\dfrac{1}{2}$ year

R = 15%

TD$ =\dfrac{BG\times 100}{TR}$

=>240 =$ \dfrac{BG \times 100}{\dfrac{1}{2} \times 15} $

$=>BG= \dfrac{240 \times 15}{100 \times 2}$

$= \dfrac{120 \times 15}{100} = Rs. 18$

BG = BD - TD

=> 18 = BD - 240

=> BD = 18 + 240 = Rs. 258

T = 3 years

R = 10%

= $\dfrac{36 \times 100}{3 \times 10} = 12 \times 10 = Rs.120$

$TD = \dfrac{PW \times TR}{100}$

=>120 = $\dfrac{PW \times 3 \times 10}{100}$

=>1200 = ${PW} \times 3$

$PW = \dfrac{1200}{3}= Rs.400$

Given that, True discount = 120
Present worth = 1200
Now,
True discount = $\sqrt {P.W.∗B.G}$
⇒ B.G. = $\dfrac{(T.d)^{2}}{P.W.}$
⇒ B.G. = $\dfrac{120 \times 120}{1200}$
⇒ B.G. = Rs. 12
Therefore, B.D. = (T.D. + B.G.) = Rs. (120 + 12) =Rs. Rs. 132

Given that,
S.I. on Rs. 1600 = T.D. on Rs. 1872
Therefore, P.W. of Rs. 1872 is Rs. 1600
Therefore, Rs.72 is S.I. on Rs. 1600 at 12%
here, B.G. = Rs. 72
Rate = 12%
T.D. = Rs. 1600
Now, consider
T.D. = $\dfrac{B.G.∗100}{Rate∗Time}$
⇒ Time = $\dfrac{B.G.∗100}{Rate∗T.D.}$
⇒ Time = $\dfrac{72∗100}{12∗1600}$
⇒ Time = $\dfrac{3}{8}years$

Given that,
Rate = 10%
Time = 10 months
Let amount of the bill = Rs. 100.
Money deducted = Rs. 20
Money received by the holder of the bill = Rs. (100 – 20) = Rs. 80.
Therefore, S.I. on Rs. 80 for 10 months = Rs. 20
Therefore, Rate =$\dfrac{B.G.∗100}{Time∗T.D}$ .
⇒ Rate = $\dfrac{20∗100}{\dfrac{10}{12}\times 80}$
⇒ Rate = 30%

B.G. = S.I. on T.D.
on Rs. ($140 \times 20 \times \dfrac{1}{2} \times \dfrac{ 1}{100}$)
= Rs. 14
Therefore, B.G. – T.D. = Rs. 14
B.G. = Rs. (140 + 14)
=Rs. 154.

Given that
B.G. = Rs. 185
Sum = Rs. 1850
Now, Sum = $\dfrac{B.G.∗T.D}{B.G.–T.D} $
= $\dfrac{B.G.∗T.D}{B.G}$
Therefore, $\dfrac{T.D}{B.G}$
= $\dfrac{sum}{B.D}$
= $\dfrac{1850}{185}$
= 10
Thus, if B.G. is Re. 1, T.D. = Rs. 10.
If B.D. is Rs. 185
T.D. = Rs.($\dfrac{10}{11} \times 185$)
= Rs. 169
B.G. = Rs. (185 – 169) = Rs. 16.