# Simple Interest

$\text{1.&space;At&space;the&space;rate&space;of}&space;\,&space;\,&space;8&space;\frac{1}{2}&space;\%&space;\,&space;\text&space;{p.a.&space;simple&space;interest,&space;a&space;sum&space;of&space;Rs.4800&space;Will&space;earn}$

$\text{how&space;much&space;interest&space;in&space;2&space;years&space;3&space;months.}$

A. 918

B. 624

C. 896

D. 789

Ans: A

Explanation:

$\text&space;{P}&space;=&space;4800$

$\text&space;{T&space;=&space;2&space;years&space;3&space;months}&space;=&space;2&space;\,&space;\frac{3}{12}&space;\,&space;\text&space;{years}&space;=&space;2\frac{1}{4}&space;\,&space;\text&space;{years}&space;=&space;\frac{9}{4}&space;\,&space;\text&space;{years}$

$\text{R}&space;=&space;8\frac{1}{2}\%&space;=&space;\frac{17}{2}\%$

$\text&space;{S.I.}&space;=&space;\frac{&space;\text&space;{PTR}}{100}&space;=&space;\frac{4800&space;\times&space;9&space;\times&space;17}{100&space;\times&space;4&space;\times&space;2}&space;=&space;918$

$\text{2.&space;What&space;will&space;be&space;the&space;simple&space;interest&space;earned&space;on&space;an&space;amount&space;of&space;Rs.16,800&space;}$

$\text{in&space;9&space;months&space;at&space;the&space;rate&space;of}&space;\,\,&space;6\frac{1}{4}\%&space;\,&space;\text{per&space;annum.}$

A. 812.50

B. 692.75

C. 954.20

D. 787.50

Ans: D

Explanation:

$\text{P}&space;=&space;16,800$

$\text{T&space;=&space;9&space;months}&space;=&space;\frac{9}{12}&space;\,&space;\text{years}&space;=&space;\frac{3}{4}&space;\,&space;\text{years}$

$\text&space;{R}&space;=&space;6\frac{1}{4}&space;\,&space;\%&space;=&space;\frac{25}{4}&space;\,&space;\%$

$\text&space;{S.I.}&space;=&space;\frac{16800&space;\times&space;3&space;\times&space;25}{100&space;\times&space;4&space;\times&space;4}&space;=&space;787.50$

3. A sum of Rs.12,500 amounts to Rs.15,500 in 4 years at The rate of simple interest. What is the rate of interest ?

A. 2%

B. 4%

C. 6%

D. 8%

Ans: C

Explanation:

$\text{P&space;=&space;12,500}$

$\text&space;{T&space;=&space;4}$

$\text{R&space;=&space;?}$

$\text{S.I.&space;=&space;A}&space;-&space;\text{P&space;=&space;15500}&space;-&space;\text{12500&space;=&space;3000}$

$\text{R}&space;=&space;\frac{3000&space;\times&space;100}{12500&space;\times&space;4}&space;=&space;6&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{R}&space;=&space;\frac{\text{S.I.}&space;\times&space;100}{\text{PT}}&space;\right&space;]$

$\text{4.&space;A&space;person&space;borrows&space;Rs.5000&space;for&space;2&space;years&space;at&space;4\%&space;p.a.&space;simple&space;Interest.}$$\text{He&space;immediately&space;lends&space;it&space;to&space;another&space;person&space;at}&space;\,&space;6&space;\frac{1}{4}\%&space;\,&space;\text{p.a.&space;for&space;2&space;years.}$

$\text{Find&space;his&space;gain&space;in&space;the&space;transaction&space;per&space;year.}$

A. 128.60

B. 141.75

C. 112.50

D. 98.95

Ans: C

Explanation:

$\text{Interest&space;on&space;A&space;borrowed}&space;=&space;\frac{5000&space;\times&space;2&space;\times&space;4}{100}&space;=&space;\text{Rs.&space;400}$

$\text{Interest&space;on&space;A&space;lend}&space;=&space;\left&space;[&space;\frac{5000&space;\times&space;2&space;\times&space;25}{100&space;\times&space;4}&space;\right&space;]&space;=&space;\text{Rs.}&space;\,&space;625$

$\text{A's&space;gain&space;in&space;the&space;transaction&space;=&space;625}&space;-&space;400&space;=&space;225$

$\text{A's&space;gain&space;per&space;one&space;year}&space;=&space;\frac{225}{2}&space;=&space;112.50$

5. A took a loan of Rs.1200 with simple interest for as many years as the rate of interest. If he paid Rs.432 as interest at the end of the loan period, what was the rate of interest ?

A. 4

B. 6

C. 8

D. 9

Ans: B

Explanation:

$\text{P}&space;=&space;1200$

$\text{Let&space;R}&space;=&space;x\%&space;\,&space;\text{then,}$

$\text{T}&space;=&space;x&space;\,&space;\text{years}$

$\text{S.I.}&space;=&space;\frac{1200&space;\times&space;x&space;\times&space;x}{100}&space;=&space;\frac{1200&space;{x}^2}{100}$

$\text{But&space;given&space;S.I.}&space;=&space;\text{Rs.}&space;\,&space;432&space;\,\,&space;\text{so,}$

$\frac{1200{x}^2}{100}&space;=&space;432$

$1200{x}^2&space;=&space;43200$

$x^{2}&space;=&space;\frac{43200}{1200}&space;=&space;36$

$x&space;=&space;\sqrt{36}&space;=&space;6$

$\therefore&space;\text{Rate&space;of&space;interest&space;=&space;6\%&space;and&space;time&space;=&space;6&space;years}$

6. A man took a loan from a bank at the rate of 12%p.a. simple interest. After 3 years he had to pay Rs.5400 interest only for the period. The principle amount borrowed by him was

A. Rs. 10000

B. Rs. 15000

C. Rs. 20000

D. Rs. 16000

Ans: B

Explanation:

$\text{S.I.}&space;=&space;5400$

$\text{T&space;=&space;3&space;years}$

$\text{R}&space;=&space;12\%$

$\text{P}&space;=&space;\frac{5400&space;\times&space;100}{3&space;\times&space;12}&space;=&space;15000&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{P}&space;=&space;\frac{\text{S.I.}&space;\times&space;100}{\text{TR}}&space;\right&space;]$

7. A sum of Rs. 800 amounts to Rs.920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to how much.

A. Rs. 820

B. Rs. 868

C. Rs. 935

D. Rs. 992

Ans: D

Explanation:

$\text{R}&space;=&space;\frac{120&space;\times&space;100}{800&space;\times&space;3}&space;=&space;5\%&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{S.I.&space;=&space;A&space;-&space;P}&space;=&space;920&space;-&space;800&space;=&space;120\right&space;]$

$\text{Rate&space;is&space;increased&space;by&space;3\%}$

$\left&space;(&space;5+3&space;\right&space;)&space;\%&space;=&space;8\%$

$\text{New&space;S.I.}&space;=&space;\frac{800&space;\times&space;3&space;\times&space;8}{100}&space;=&space;192$

$\text{New&space;Amount}&space;=&space;800&space;+&space;192&space;=&space;992$

8. A sum of Rs.1550 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs.106 find the money lent at each rate.

A. Rs.650, Rs.900

B. Rs.750, Rs.800

C. Rs.680, Rs.950

D. Rs.800, Rs. 950

Ans: A

Explanation:

$\text{Let&space;the&space;sum&space;lent&space;at&space;8\%&space;be&space;Rs.}\,&space;x&space;\,&space;\text{and&space;that&space;at&space;6\%&space;be&space;Rs.}\left&space;(&space;1550&space;-&space;x&space;\right&space;)$

$\left&space;[&space;\frac{x&space;\times&space;8&space;\times&space;1}{100}&space;\right&space;]&space;+&space;\left&space;[&space;\frac{\left&space;(&space;1550&space;-&space;x&space;\right&space;)&space;\times&space;6&space;\times&space;1}{100}&space;\right&space;]&space;=&space;106$

$\frac{8x}{100}&space;+&space;\frac{9300&space;-&space;6x}{100}&space;=&space;106$

$\frac{8x&space;+&space;9300&space;-&space;6x}{100}&space;=&space;106$

$\frac{2x&space;+&space;9300}{100}&space;=&space;106$

$2x&space;+&space;9300&space;=&space;10600$

$x&space;=&space;\frac{1300}{2}&space;=&space;650$

$\text{Money&space;lend&space;at&space;8\%}&space;=&space;\text{Rs.}&space;650$

$\text{Money&space;lend&space;at&space;6\%}&space;=&space;1550&space;-&space;650&space;=&space;\,&space;\text{Rs.}&space;900$

9. At what rate percent of simple interest will a sum of money double itself in 12 years.

$\text{A.}&space;8&space;\frac{1}{3}\%$

$\text{B.}&space;8\frac{1}{4}\%$

$\text{C.}&space;9&space;\frac{1}{2}\%$

$\text{D.}&space;9&space;\frac{1}{4}\%$

Ans: A

Explanation:

$\text{Let&space;P}&space;=&space;x&space;\,\,\text{then&space;S.I.}&space;=&space;x$

$\text{T&space;=&space;12&space;years}$

$\text{R}&space;=&space;\,&space;?$

$\text{R}&space;=&space;\frac{x&space;\times&space;100}{x&space;\times&space;12}&space;=&space;\frac{100}{12}&space;=&space;8\frac{1}{3}\%&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{R}&space;=&space;\frac{\text{S.I.}&space;\times&space;100}{\text{P}&space;\times&space;\text{T}}&space;\right&space;]$

10. Ram borrowed some money at the rate of 6% p.a. for the first three years 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs.8160, how much money did he borrow ?

A. Rs.6000

B. Rs.7000

C. Rs.8000

D. Rs.9000

Ans: C

Explanation:

$\text{Let&space;P&space;be&space;the&space;principle}$

$\text{S.I.}&space;=&space;\left&space;[&space;\frac{p&space;\times&space;6&space;\times&space;3}{100}&space;\right&space;]&space;+&space;\left&space;[&space;\frac{p&space;\times&space;9&space;\times&space;5}{100}&space;\right&space;]&space;+&space;\left&space;[&space;\frac{p&space;\times&space;13&space;\times&space;3}{100}&space;\right&space;]$

$=&space;\frac{18p}{100}&space;+&space;\frac{45p}{100}&space;+&space;\frac{39p}{100}$

$=&space;\frac{18p&space;+&space;45p&space;+&space;39p}{100}$

$=&space;\frac{102p}{100}$

$\text{Given&space;S.I.}&space;=&space;8160$

$\frac{102p}{100}&space;=&space;8160$

$\text{P}&space;=&space;8160&space;\times&space;\frac{100}{102}&space;=&space;8000$