# 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. $T.D=\sqrt{P.W\times B.G}$**

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

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

**6. $Amount=\frac{B.D\times T.D}{B.D-T.D}$**

**7. $T.D=\frac{B.G\times 100}{Rate\times Time}$**

A) Rs. 24 | B) Rs. 12 |

C) Rs. 36 | D) Rs. 18 |

Explanation:

T= 6 months = 1/2 year

R = 6%

$TD=\frac{BD\times 100}{100+TR}=\frac{18.54\times 100}{100+\left({\displaystyle \frac{1}{2}}\times 6\right)}=Rs.18$

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.

A) 78 | B) 96 |

C) 105 | D) 85 |

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.

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 |

Explanation:

BD = Rs.100

TD = Rs.80

R = 10%

$F=\frac{BD\times TD}{BD-TD}=\frac{100\times 80}{100-80}=Rs.400$

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

$\Rightarrow 100=\frac{400\times T\times 10}{100}\phantom{\rule{0ex}{0ex}}$

=> T = 2.5 years

A) Rs. 2 | B) Rs. 1.25 |

C) Rs. 2.25 | D) Rs. 0.5 |

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

$BD=\frac{FTR}{100}=\frac{8100\times {\displaystyle \frac{1}{4}}\times 5}{100}=Rs.101.25$

$TD=\frac{FTR}{100+TR}=\frac{8100\times {\displaystyle \frac{1}{4}}\times 5}{100+\left({\displaystyle \frac{1}{4}}\times 5\right)}=Rs.100$

Therefore BD - TD = 101.25-100 = Rs.1.25

A) 15 | B) 16 |

C) 14 | D) 13 |

A) 8 months | B) 11 months |

C) 10 months | D) 9 months |

Explanation:

F = Rs. 498

TD = Rs. 18

PW = F - TD = 498 - 18 = Rs. 480

R = 5%

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

$\Rightarrow 18=\frac{480\times T\times 5}{100}$

=> T = 3/4 years = 9 months