Free Practice Questions for Simple-and-compound-interest in Maths

Principal:- Rs. 80000

Rate $:10+5+\frac{10\times 5}{100}$

Time :- 2 years

$\begin{array}{rl}\text{ Interest }& =\text{ Rs. }80000\times \frac{15.5}{100}\\ & =\text{ Rs. }12,400\\ \text{ Amount }& =80,000+12,400\\ & =\text{ Rs. }92,400\end{array}$

Let principal be $p$

Rate of interest is $40\mathrm{\%}$ p.a.

And time $=3$ year

$\begin{array}{rl}\text{ After }3\text{ years total simple interest }& =\frac{p\times 40\times 3}{100}\\ & =\frac{6p}{5}\end{array}$

$\begin{array}{rl}\text{ Amount after }3\text{ year }& =\frac{6p}{5}+\mathrm{p}\\ & =\frac{11p}{5}\end{array}$

Now, according to the given condition,

$\begin{array}{rl}\frac{11p}{5}& =9900\\ \mathrm{p}& =\frac{9900\times 5}{11}\\ \mathrm{p}& =\text{ Rs. }4500\end{array}$

The principal amount invested by Mohit was Rs. 4500

S.I $=18\mathrm{\%}\times 3$

$=54\mathrm{\%}$

Rs. $8,100=54\mathrm{\%}$

Rs. $37,500=\frac{54\mathrm{\%}}{8,100}\times 37,500=250\mathrm{\%}$

$\mathrm{RT}\mathrm{\%}=250\mathrm{\%}$

$\mathrm{R}\times 8=250$

$\mathrm{R}=31.25\mathrm{\%}$

ATQ,

Let salary of Ankit is 1000 units.

Interest of 2 years - 

300               10%   -   30

                                 -  30 $$3

CI after 2 years = 63 units

63 units = 5670

1 unit = 90

1000 units = 90000

$\begin{array}{rl}\text{ Expenditure }& =90,000\times \frac{1}{3}\\ & =30,000\end{array}$

2.5 units = 1000

1 unit = 400

Sum = 100 × 400

= 40000

Given
Amount = ₹37,632
Rate = 12%
Time (T) =2 years
$A=P{(1+\frac{R}{100})}^t$
$37632=P{(1+\frac{12}{100})}^2$
$37632=P{\left(\frac{112}{100}\right)}^2$
$37632=P{\left(\frac{28}{25}\right)}^2$
$P=\frac{37632\times 25\times 25}{28\times 28}$
P= 30,000
According to question
S.I. $=\frac{PRT}{100}$
S.I. $=\frac{30000\times 12\times 4}{100}$
S.I. = 14400

Given Principal amount $\mathrm{P}=$ Rs 500
Time period $\mathrm{T}=4$ years
Rate of interest $\mathrm{R}=8\mathrm{\%}$ p.a.
We know that simple interest $=\frac{(P\times R\times T)}{100}$
On substituting these values in the above equation we get
$\mathrm{SI}=\frac{(500\times 8\times 4)}{100}$
$=\mathrm{Rs}160$
Amount $=$ Principal amount $+$ Interest
$=\mathrm{Rs}500+160$
$=\mathrm{Rs}660$

Interest $=5,310-4500=810$
$810=\frac{P\times R\times T}{100}$
$\Rightarrow 810=\frac{4500\times R\times 4}{100}$
$\Rightarrow \mathrm{R}=\frac{810}{180}$
$\Rightarrow \mathrm{R}=4.5\mathrm{\%}$

We know SI for the each year is same so we can write it as:

                              SI                 CI

For 1st year  =     6400             6400

For 2nd year =    6400             6400+704

Let x be the required rate.

According to question,

6400 of  x% =704
$6400\times \frac{x}{100}=704$

$\mathrm{x}=\frac{704}{64}=11\mathrm{\%}$

Rate of SI for two year $=10+10=20\mathrm{\%}$
Rate of CI for two year $=10+10+\frac{10\times 10}{100}=21\mathrm{\%}$
Given, $(21-20)\mathrm{\%}=1200$
$\begin{array}{rl}1\mathrm{\%}& =1200\\ 100\mathrm{\%}& =1,20,000\end{array}$

Let

 The rate of interest per annum is $r_1$ , $r_2$ , $r_3$ respectively

According to Question

$r_1=5\mathrm{\%}=\frac{1}{20}{r}_2=6\mathrm{\%}=\frac{3}{50}{r}_3=8\mathrm{\%}=\frac{2}{25}$

First-year ratio $=20:21$

Second year ratio $=50:53$

Third year ratio $=25:27$

Ratio of principle to Amount $=20\times 50\times 25:21\times 53\times 27$ $=25000:30051$

If the Amount is $=Rs.30,051$

Then Principle $=Rs.25,000$

Rate for 8 months $=15\mathrm{\%}\times \frac{8}{12}=10\mathrm{\%}$
Let share of $A$ is $=A$
2 years $=24$ months $=8\times 3$ months
$n=3$
After 2 years share of $A=A{(1+\frac{10}{100})}^3$
Let share of $B$ is $=B$
$2\frac{2}{3}$ years $=32$ months $=8\times 4$ months

$n=3$
After $2\frac{2}{3}$ years share of $B=B{(1+\frac{10}{100})}^4$
A : B
$\mathrm{A}{(1+\frac{10}{100})}^3:\mathrm{B}{(1+\frac{10}{100})}^4$
$\frac{A}{B}=(1+\frac{10}{100})$
$\frac{A}{B}=\frac{11}{10}$
A = $11x$
B = $10x$
$21x$ = ₹ $8,400$
$x$ = ₹ $400$
Share of A = $11x$
$=11\times$₹ $400$
= ₹ $4,400$

Principal $=$₹ 20,000
Rate $=9\mathrm{\%}$ p.a.
Time $=1$ year and 4 months
Compound interest for 1 year $=9\mathrm{\%}$ of ₹ 20,000=₹ 1800
After 1 year amount $=$₹ 21,800
Compound interest for 4 months
Rate $=9\mathrm{\%}\times \frac{4}{12}=3\mathrm{\%}$
Principal = ₹ 21,800
Compound interest for 4 months = 3% of ₹ 21,800 = ₹ 654
Total compound interest for 1 year and 4 months $=$₹ 1800+₹ 654 = ₹ 2,454

$\begin{array}{rl}& 2\text{ year }\mathrm{Cl}\text{ and SI difference }=\frac{r^2}{100}\mathrm{\%}\\ & =\frac{5^2}{100}\mathrm{\%}\\ & =0.25\mathrm{\%}\text{ of }6,000\\ & \text{ = ₹ }15\\ & \end{array}$

R1 = 8%
R2 = 10%
R3 = 12%
Total interest in $\mathrm{\%}=\mathrm{R}1+\mathrm{R}2+\mathrm{R}3+\frac{R1R2+R2R3+R3R1}{100}+\frac{R1R2R3}{10000}$
$=8\mathrm{\%}+10\mathrm{\%}+12\mathrm{\%}+\frac{8\mathrm{\%}+10\mathrm{\%}+12\mathrm{\%}}{100}+\frac{8\times 10\times 12}{10000}$
$=33.056\mathrm{\%}$
Compound interest in Rupees =33.056 % of ₹ 10,000
=₹ 3,305.6

Simple interest at $5\mathrm{\%}=\frac{14000\times 5\times 3}{100}=$₹ 2100
Simple interest at $6\mathrm{\%}=\frac{19000\times 6\times 3}{100}=$₹ 3420
Total income from the interest in 3 years $=2100+3420=$₹ 5520

Let the principle be x

so, amount be 2x

Interest = 2x-x = x

$\mathrm{X}=\frac{x\times 6\times r}{100}$
$\mathrm{r}=\frac{50}{3}\mathrm{\%}$

When amount is = 5x

Interest = 5x-x = 4x

$4\mathrm{x}=\frac{x\times t\times 50}{100\times 3}$
$\mathrm{t}=24$ years

$\begin{array}{rl}& \text{ Rate }=\frac{16}{2}=8\mathrm{\%}\\ & \text{ Amount }=\mathrm{P}{(1+\frac{r}{100})}^t\\ & 5832=5000{(1+\frac{8}{100})}^t\\ & \frac{5832}{5000}={\left(\frac{54}{50}\right)}^t\\ & {\left(\frac{54}{50}\right)}^2={\left(\frac{54}{50}\right)}^t\\ & \mathrm{T}=2\end{array}$
Interest is compounded half yearly
So required time $=\frac{2}{1}=2$

Difference between CI and SI for 2 year $=\mathrm{P}{\left(\frac{r}{100}\right)}^2$
$\mathrm{P}{\left(\frac{r}{100}\right)}^2=152$
$\mathrm{P}{\left(\frac{5}{100}\right)}^2=152$
$\mathrm{P}\times \frac{1}{20}\times \frac{1}{20}=152$
$\mathrm{P}=152\times 20\times 20$
$\mathrm{P}=$₹ 60800