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Q:

The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

A) Rs. 432 B) Rs. 422
C) Rs. 412 D) Rs. 442

Answer:   A) Rs. 432

Explanation:

F = Rs. 2160

TD = Rs. 360

PW = F - TD = 2160 - 360 = Rs. 1800

True Discount is the Simple Interest on the present value for unexpired time

=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360

Banker's Discount is the Simple Interest on the face value of the bill for unexpired time

= Simple Interest on Rs. 2160 for unexpired time

=(360/1800)* 2160

= (1/5) * 2160

=Rs. 432

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%

\inline {\color{Blue}F=\frac{BD\times TD}{BD-TD}=\frac{100\times 80}{100-80}=\frac{100\times 80}{20}=Rs.400}

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

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

\inline {\color{Blue}\Rightarrow 100=\frac{400\times T\times 10}{100}}

\inline {\color{Blue}\Rightarrow 100=4\times T\times 10}

\inline {\color{Blue}\Rightarrow 10=4\times T}

\inline {\color{Blue}\Rightarrow T=\frac{10}{4}=2.5 years}

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2 444
Q:

If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?

A) 8 months B) 11 months
C) 10 months D) 9 months
 
Answer & Explanation Answer: D) 9 months

Explanation:

F = Rs. 498

TD = Rs. 18

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

R = 5%

\inline {\color{Blue} TD=\frac{PW\times TR}{100}}

\inline {\color{Blue} \Rightarrow 18=\frac{480\times T\times 5}{100}}

\inline {\color{Blue} \Rightarrow 18=24\times T}

\inline {\color{Blue} \Rightarrow T=\frac{18}{24}=\frac{3}{4}years=\frac{12\times 3}{4}months=9months}

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1 495
Q:

What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5%

A) Rs. 2 B) Rs. 1.25
C) Rs. 2.25 D) Rs. 0.5
 
Answer & Explanation Answer: B) Rs. 1.25

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

\inline {\color{Blue} BD=\frac{FTR}{100}=\frac{8100\times \frac{1}{4}\times 5}{100}=\frac{2025}{20}=\frac{405}{4}=Rs.101.25}

\inline {\color{Blue} TD=\frac{FTR}{100+TR}=\frac{8100\times \frac{1}{4}\times 5}{100+(\frac{1}{4}\times 5)}=\frac{2025\times 5}{100+(\frac{5}{4})}}

\inline {\color{Blue} =\frac{2025\times 5\times 4}{400+5}=\frac{2025\times 5\times 4}{405}=\frac{405\times 5\times 4}{81}=\frac{45\times 5\times 4}{9}=Rs.100}

\inline {\color{Blue} BD-TD=Rs.101.25 -Rs.100=Rs.1.25}

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1 491
Q:

The banker's discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?

A) Rs. 24 B) Rs. 12
C) Rs. 36 D) Rs. 18
 
Answer & Explanation Answer: D) Rs. 18

Explanation:
T= 6 months = 1/2 year

R = 6%

\inline {\color{Blue} TD=\frac{BD\times 100}{100+TR}=\frac{18.54\times 100}{100+(\frac{1}{2}\times 6)}=\frac{18.54\times 100}{103}=\frac{1854}{103}=Rs.18}

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0 793
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
 
Answer & Explanation Answer: D) Rs. 200

Explanation:

\inline {\color{Blue} F=\frac{BD\times TD}{BD-TD}=\frac{200\times 100}{200-100}=\frac{200\times 100}{100}=Rs.200}

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