0
Q:

# What is the present worth of a bill of Rs.1764 due 2 years hence at 5% compound interest is

 A) Rs. 1600 B) Rs. 1200 C) Rs. 1800 D) Rs. 1400

Explanation:

Since the compound interest is taken here,

$\inline&space;{\color{Black}&space;PW(1+\frac{5}{100})^{2}=1764}$

$\inline&space;{\color{Black}&space;PW(1+\frac{1}{20})^{2}=1764}$

$\inline&space;{\color{Black}&space;PW(\frac{21}{20})^{2}=1764}$$\inline&space;{\color{Black}&space;PW\times&space;\frac{441}{400}=1764}$

$\inline&space;{\color{Black}&space;\Rightarrow&space;PW=\frac{1764\times&space;400}{441}=4\times&space;400=Rs.1600}$

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%

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

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 =

$\inline&space;{\color{Blue}\Rightarrow&space;100=\frac{400\times&space;T\times&space;10}{100}}$

$\inline&space;{\color{Blue}\Rightarrow&space;100=4\times&space;T\times&space;10}$

$\inline&space;{\color{Blue}\Rightarrow&space;10=4\times&space;T}$

$\inline&space;{\color{Blue}\Rightarrow&space;T=\frac{10}{4}=2.5&space;years}$

2 519
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

Explanation:

F = Rs. 498

TD = Rs. 18

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

R = 5%

$\inline&space;{\color{Blue}&space;TD=\frac{PW\times&space;TR}{100}}$

$\inline&space;{\color{Blue}&space;\Rightarrow&space;18=\frac{480\times&space;T\times&space;5}{100}}$

$\inline&space;{\color{Blue}&space;\Rightarrow&space;18=24\times&space;T}$

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

1 571
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

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

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

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

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

$\inline&space;{\color{Blue}&space;BD-TD=Rs.101.25&space;-Rs.100=Rs.1.25}$

1 588
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

Explanation:
T= 6 months = 1/2 yearR = 6%

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

0 950
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:

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