# 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 B.D. and T.D. on a certain sum is Rs.200 and Rs.100 respectively. Find out the sum.

 A) Rs. 400 B) Rs. 300 C) Rs. 100 D) Rs. 200

Explanation:

$F=BD×TDBD-TD=200×100200-100=200×100100=Rs.200$

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Q:

The bankers 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) 4 months B) 5 months C) 6 months D) 3 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 * 72)/(12 * 1800)

= 1/3 years = 4 months