# Banker's Discount Questions

FACTS  AND  FORMULAE  FOR  BANKER'S  DISCOUNT  QUESTIONS

Banker's Discount :

Suppose a merchant 'A' buys goods worth, say Rs. 10,000 from another merchant 'B' at a credit of say 5 months.Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months.

The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it to get a date, known as legally due date.

Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e , paid by the banker) and the legally due date. This amount is known as Banker's Discount (B.D) Thus, B.D is the S.I on the face value for the period from the date on which the bill was discounted and the legally due date.

Banker's Gain (B.G) = (B.D) - (T.D) for the unexpired time.

Note : When the date of the bill is not given, grace days are not to be added.

IMPORTANT FORMULAE

1. B.D = S.I on bill for unexpired time

2. B.G = (B.D) - (T.D) = S.I  on $T.D=\frac{{\left(T.D\right)}^{2}}{P.W}$

3. $T.D=\sqrt{P.W×B.G}$

4. $B.D=\left(\frac{Amount×Rate×Time}{100}\right)$

5. $T.D=\left[\frac{Amount×Rate×Time}{100+\left(Rate×Time\right)}\right]$

6. $Amount=\frac{B.D×T.D}{B.D-T.D}$

7. $T.D=\frac{B.G×100}{Rate×Time}$

Q:

The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs.

16. The true discount is:

 A) 78 B) 96 C) 105 D) 85

Explanation:

T.D. = P.W. x B.G. = 576 x 16 = 96.

Filed Under: Banker's Discount

0 10014
Q:

The banker's discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs. 1872 for the same time at the same rate. Find the time.

 A) 7 months B) 6 months C) 3 months D) 4 months

Explanation:

S.I. on Rs. 1800 = T.D. on Rs. 1872.

P.W. of Rs. 1872 is Rs. 1800.

Rs. 72 is S.I. on Rs. 1800 at 12%.

Time =[(100 x 72)/ (12x1800)]year

=1/3year = 4 months.

Filed Under: Banker's Discount

3 9847
Q:

The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is

Rs. 160. The banker's gain is:

 A) 15 B) 16 C) 14 D) 13

Explanation:

B.G. =(T.D.)^2/P.W.

= Rs. (160*160)/1600 = Rs. 16.

Filed Under: Banker's Discount

1 7917
Q:

If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?

 A) 50 B) 129 C) 100 D) 160

Explanation:

B.G. = S.I. on T.D.

= Rs.(120 x 15 x 1/2 x 1/100)

= Rs. 9.

(B.D.) - (T.D.) = Rs. 9.

B.D. = Rs. (120 + 9) = Rs. 129.

Filed Under: Banker's Discount

3 7828
Q:

A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.

 A) 4390 B) 6580 C) 5880 D) 5350

Explanation:

Face value of the bill = Rs. 6000.

Date on which the bill was drawn = July 14 at 5 months. Nominally due date =                  December 14.

Legally due date = December 17.

Date on which the bill was discounted = October 5.

Unexpired time  : Oct.               Nov.                Dec.

26  +               30  +              17     = 73 days  =1/ 5Years

B.D. = S.I. on Rs. 6000 for 1/5 year

= Rs.   (6000 x 10 x1/5 x1/100)= Rs. 120.

T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]

=Rs.(12000/102)=Rs. 117.64.

B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.

Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.

Filed Under: Banker's Discount

5 7643
Q:

The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain.

 A) 15 B) 20 C) 18 D) 13

Explanation:

Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]

= [(B.D.xT.D.)/B.G.]

T.D./B.G.  = Sum/ B.D.

=1650/165

=10

Thus, if B.G. is Re 1, T.D. = Rs. 10.

If B.D.is Rs. ll, T.D.=Rs. 10.

If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]

=Rs.150

And, B.G. = Rs. (165 - 150) = Rs, 15.

Filed Under: Banker's Discount

6 6722
Q:

The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?

 A) Sum = Rs.400 and Time = 5 years B) Sum = Rs.200 and Time = 2.5 years C) Sum = Rs.400 and Time = 2.5 years D) Sum = Rs.200 and Time = 5 years

Answer & Explanation Answer: C) Sum = Rs.400 and Time = 2.5 years

Explanation:

BD = Rs.100

TD = Rs.80

R = 10%

$F=BD×TDBD-TD=100×80100-80=Rs.400$

BD = Simple interest on the face value of the bill for unexpired time= FTR/100

$⇒100=400×T×10100$

=> T = 2.5 years

Filed Under: Banker's Discount

4 6426
Q:

Two consecutive discounts x% and y% is equivalent to the discount

 A) (x-y+xy100)% B) (x+y+xy100)% C) (x-y-xy100)% D) (x+y-xy100)%