Tag: mathematics and statistics

Quizzes (38) Questions (955)

Questions Related to mathematics and statistics

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A four year Indira Vikas certificate with a maturity value of Rs. 700 is purcahsed for Rs. 500. The rate $\%$ p.a. is :

  1. $

    9 \dfrac { 1 } { 11 } \%

    $
  2. $10\%$
  3. $11\%$
  4. $

    21 \dfrac { 9 } { 11 } \%

    $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Interest $= 200.....(700-500=200)$


$SI=\dfrac{P\times N\times R}{100}$

$200=\dfrac{500 \times R \times 4}{100}\implies R=10\%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate per cent per annum, will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?

  1. 25

  2. 23

  3. 20

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Principal = Rs.32000 
Amount $= Rs.(32000 + 5044) = Rs.37044$
Rate $= r\%$ p.a. or $\displaystyle \cfrac{r}{4}\%$ per quarter 
Time = 9 months = 3 quarters i.e., $n = 3$
$\displaystyle \therefore$ Applying $\displaystyle A=P\left ( 1+\cfrac{r}{100} \right )^{n}$ we have
$\displaystyle 37044=32000\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \cfrac{37044}{32000}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow \cfrac{9261}{8000}=\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \left ( \cfrac{21}{20} \right )^{3}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow 1+\cfrac{r}{400}=\cfrac{21}{20}\Rightarrow \cfrac{r}{400}=\cfrac{21}{20}-1=\cfrac{1}{20}\Rightarrow r=\cfrac{400}{20}=20\%p.a.$
Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate of interest per annum will a sum double itself in 8 years?

  1. $25\%$
  2. $6\frac{1}{4} \%$
  3. $12\frac{1}{2} \%$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

T = 8 years; N = 2; R = ?
R $\times T$ = 100 $\times (N - 1)$


R $\times 8$= 100 $\times (2 - 1)$

$R\, =\, \displaystyle \frac {100}{8}\, =\, 12\frac{1}{2}\, \%$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Simple interest on Rs.2000 for 4 years is Rs.400. Percent rate of interest is

  1. $\displaystyle\frac{2000\times 100}{400\times 4}$
  2. $\displaystyle\frac{400\times 4}{2000\times 100}$
  3. $\displaystyle\frac{400\times 100}{2000\times 4}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Principal = Rs 2000
Time = 4 years
Interest = Rs 400
Now, $Interest = \frac{Principal \times Rate \times Time}{100}$
$400 = \frac{2000\times R\times 4}{100}$
$R = \frac{400 \times 100}{2000 \times 4}$

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?

  1. $4\frac {1}{2}$%
  2. $5\frac {1}{2}$%

  3. 4%

  4. 5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$SI=\frac {2}{5}P, t=10, r=?$
$\frac {Ptr}{100}=\frac {2}{5}P$
or $\frac {10\times r}{100}=\frac {2}{5}$
or $r=\frac {20}{5}=4$%

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

A person finds that an increase in the rate of interest from $\displaystyle4\frac{7}{8}$% to $\displaystyle5\frac{1}{8}$% per annum increases his yearly income by Rs 30. His capital in rupees is

  1. 15,000

  2. 14,000

  3. 13,000

  4. 12,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

increase in rate of interest

$4\frac { 7 }{ 8 } =\frac { 39 }{ 8 } $
$5\frac { 1 }{ 8 } =\frac { 41 }{ 8 } $
$\frac { 41 }{ 8 } -\frac { 39 }{ 8 } =\frac { 2 }{ 8 } $
$\frac { 2 }{ 8 } $% of income is Rs30 of the capital
$1$% of income is $\frac { 8 }{ 2 } \times 30$ of capital
$100$% of income will be$\frac { 8 }{ 2 } \times 30\times 100=12000$
His capital in rupees is 12000

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

Anil invests Rs 3,000 for a year and Sunil joins him with Rs 2,000 after 4 months. After the year they receive a return of Rs 2,600. Sunil's share is

  1. Rs 800

  2. Rs 1,000

  3. Rs 750

  4. Rs 900
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Ratio\quad in\quad which\quad they\quad should\quad share\quad their\quad profits=Raio\quad of\quad investments\times \quad Time\quad period$

$=\frac { 3000\times 12 }{ 2000\times 8 } =\frac { 3\times 3 }{ 2\times 2 } =\frac { 9 }{ 4 } $
Sunils share will be$=\frac { 4 }{ 13 } \times 2600=800$
Sunils share will be Rs800,

Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

The time required so that Rs 450 may increase to Rs 576 (the rate of simple interest being 7% per annum) is

  1. 2 years

  2. 3 years

  3. 4 years

  4. 6 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Simple interest will be(576-450)=Rs126

 Let the Time required  be t
As per formula,
$Simple\quad Interest=\frac { P\times t\times r }{ 100 } $
$126=\frac { 450\times t\times 7 }{ 100 } $
$315t=1260$
$t=\frac { 1260 }{ 315 } =4$
Time required will be 4 years


Multiple choice mathematics and statistics banks and simple interest introduction to interests introduction to interest introduction to interest payments

If the simple interest on a certain sum of money is $\displaystyle \frac{4}{25}$th of the sum and the rate per cent equals the number of years, then the rate of interest per annum is

  1. $2$%
  2. $4$%
  3. $5$%
  4. $6$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$   Let the principal be $Rs.x$.

$\Rightarrow$   Then, Simple Interest = $\dfrac{4}{25}x.$
$\Rightarrow$    Let the rate of interest per annum be $r\%$ then time ( T)= $r$ years.
$\Rightarrow$   $R=\dfrac{100\times S.I.}{P\times T}$

$\Rightarrow$   $r=\dfrac{100\times \dfrac {4x}{25}}{x\times r}$

$\Rightarrow$   $r^2=\dfrac{400}{25}$

$\Rightarrow$   $r=\dfrac{20}{5}=4\%$