Tag: mathematics and statistics

Questions Related to mathematics and statistics

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

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

  1. $

    9 \dfrac { 1 } { 11 } \%

    $

  2. $10\%$

  3. $11\%$

  4. $

    21 \dfrac { 9 } { 11 } \%

    $

Show answer
Correct Option: B
Explanation:

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


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

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

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

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

  1. 25

  2. 23

  3. 20

  4. 18

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Correct Option: C
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
$\displaystyle 37044=32000\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \cfrac{37044}{32000}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow \cfrac{9261}{8000}=\left ( 1+\cfrac{r}{400} \right )^{3}\Rightarrow \left ( \cfrac{21}{20} \right )^{3}=\left ( 1+\cfrac{r}{400} \right )^{3}$
$\displaystyle \Rightarrow 1+\cfrac{r}{400}=\cfrac{21}{20}\Rightarrow \cfrac{r}{400}=\cfrac{21}{20}-1=\cfrac{1}{20}\Rightarrow r=\cfrac{400}{20}=20\%p.a.$

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

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

  1. $25\%$

  2. $6\frac{1}{4} \%$

  3. $12\frac{1}{2} \%$

  4. None

Show answer
Correct Option: C
Explanation:

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


R $\times 8$= 100 $\times (2 - 1)$

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

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

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

  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

Show answer
Correct Option: C
Explanation:

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

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

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

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

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

  3. 4%

  4. 5%

Show answer
Correct Option: C
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 $r=\frac {20}{5}=4$%

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

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

  1. 15,000

  2. 14,000

  3. 13,000

  4. 12,000

Show answer
Correct Option: D
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

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

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

  1. Rs 800

  2. Rs 1,000

  3. Rs 750

  4. Rs 900

Show answer
Correct Option: A
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,

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

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

  1. 2 years

  2. 3 years

  3. 4 years

  4. 6 years

Show answer
Correct Option: C
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


The _______ is the percentage of a sum of money charged for its use.

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

  1. principal

  2. interest

  3. rate of interest

  4. amount

Show answer
Correct Option: C
Explanation:

The rate of interest is the percentage of a sum of money charged for its use.

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

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

  1. $2$%

  2. $4$%

  3. $5$%

  4. $6$%

Show answer
Correct Option: B
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.
$\Rightarrow$   $R=\dfrac{100\times S.I.}{P\times T}$

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

$\Rightarrow$   $r^2=\dfrac{400}{25}$

$\Rightarrow$   $r=\dfrac{20}{5}=4\%$