Tag: mathematics and statistics

Questions Related to mathematics and statistics

The difference between compound interest and simple interest at the same rate on Rs.5000 for 2 years is Rs.72 What is the rate of interest per annum ?

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

  1. 20

  2. 15

  3. 12

  4. 10

Show answer
Correct Option: C
Explanation:
Let the rate per cent p.a.be r. Then,
$\displaystyle S.I.=Rs.\left ( 5000\times \cfrac{r}{100}\times 2 \right )=Rs.100r$
$\displaystyle C.I.=Rs.\left [ 5000\left ( 1+\cfrac{r}{100} \right )^{2}-5000 \right ]$
$=Rs.5000\left [ \left ( 1+\cfrac{r}{100} \right )^{2}-1 \right ]$
$=Rs.5000\left [ \left ( 1+\cfrac{r^{2}}{10000}+\cfrac{2r}{100} \right )-1 \right ]$
$\displaystyle =Rs.5000\left ( \cfrac{r^{2}}{10000}+\cfrac{r}{50} \right )=Rs.\cfrac{5000(r^{2}+200r)}{10000}$
$=Rs.\left ( \cfrac{r^{2}}{2}+100r \right )$
$\displaystyle \therefore C.I.-S.I.=72$
$\displaystyle \Rightarrow \cfrac{r^{2}}{2}+100r-100r=72$
$\Rightarrow \cfrac{r^{2}}{2}=72$ 
$\Rightarrow r^{2}=144$
$\Rightarrow r=12\%\: \: p.a.$

A sum of money amounts to Rs.4840 in 2 years and Rs.5324 in 3 years at compound interest compounded annually. What is the rate of interest per annum ?

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

  1. 8

  2. 10

  3. 12

  4. 15

Show answer
Correct Option: B
Explanation:

 Let the principal be Rs.P and rate of interest p.a. = r% Then
$\displaystyle P\left ( 1+\frac{r}{100} \right )^{2}=4840...........(i)$ and $\displaystyle P\left ( 1+\frac{r}{100} \right )^{3}=5324...........(ii)$
$\displaystyle \Rightarrow \frac{5324}{4840}=\frac{(1+r/100)^{3}}{(1+r/100)^{2}}\Rightarrow 1+\frac{r}{100}=\frac{1331}{1210}$
$\displaystyle \Rightarrow \frac{r}{100}=\frac{1331}{1210}-1=\frac{121}{1210}=\frac{1}{10}\Rightarrow r=\frac{1}{10}\times 100=10\%: p.a.$

A certain sum of money amounts to $\displaystyle \frac {5}{4}$ of itself in 5 years. The rate percent per annum is

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

  1. 5%

  2. 7%

  3. 9%

  4. 12%

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Correct Option: A
Explanation:

R $\times$ T = 100 $\times$ (N - 1)
$R \times 5 = 100 \times \left ( \displaystyle \frac {5}{4} - 1 \right )$
$R \times 5 = 100 \times \displaystyle \frac {1}{4}$
$R = 5\%$

Madhav lent out Rs. 7953 for 2 years and Rs. 1800 for 3 years at the same rate of simple interest. If he got Rs. 2343. 66 as total, then find the percent rate of interest.

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

  1. 11%

  2. 12%

  3. 12.5%

  4. 5%

Show answer
Correct Option: A
Explanation:

We know that Simple Interest $ = \cfrac {PNR}{100} $
Given,  $ \cfrac {7953 \times 2 \times R}{100}  + \cfrac {1800  \times 3 \times R}{100}  = Rs 2343.66 $
$=> 159.06R + 54R = Rs 2343.66 $
$ => 213.06R = 2343.66 $
$ => R = 11 \%$ 

Madhav lent out Rs $7953$ for $2$ years and Rs $1800$ for $3$ years at the same rate of simple interest. If he hot Rs $2343.66$ as total interest then find the percent rate of interest.

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

  1. $11\%$

  2. $12\%$

  3. $12.5\%$

  4. $5\%$

Show answer
Correct Option: A
Explanation:

$S.I = \dfrac{P\times t\times r}{100}$


Let the rate be $r$ Principal $P$ and time $t$

${S.I} _{1}=\dfrac{7953\times 2\times r}{100}$


${S.I} _{2}=\dfrac{1800\times 3\times r}{100}$
$Total$ $simple$ $interest = {S.I} _{1}+{S.I} _{2} $

$2343.66=\dfrac { 7953\times2\times r }{ 100 } +\dfrac { 1800\times3\times r }{ 100 }$ 
$2343.66 = 213.06\times r$
$r = 11\%$

If the interest is payable quarterly, Rs. $1600$ amounts to Rs. $2662$ after $1\dfrac{1}{2}$ years, the annual rate of interest is

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

  1. $5\%$

  2. $10\%$

  3. $20\%$

  4. $35\%$

Show answer
Correct Option: D
Explanation:

Amount $= Rs. 2662$
Principal $= Rs. 1600$
Time $= 1.5$ years $= 6$ quarters
$A = P\left(1 + \cfrac{R}{100}\right)^T$
$2662 = 1600 \left(1 + \cfrac{R}{100}\right)^6$
$1.088 = 1 + \cfrac{R}{100}$
$R = 8.8\%$
Hence, annual rate of interest $=8.8\times 4 = 35\%$

Find the rate, when 1,800 earns an interest of Rs 432 in 3 years

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

  1. 7%

  2. 6%

  3. 5%

  4. 8%

Show answer
Correct Option: D
Explanation:

Given $P=1, 800, SI=432, T=3 years$
$R=\dfrac {SI\times 100}{P\times T}=\dfrac {432\times 100}{1800\times 3}=8$%

Rajan borrowed Rs. $50,000$ from Rakesh at simple interest. After $3$ years, Rakesh got Rs. $3000$ more than what he had given to Rajan. What was the rate of interest per annum?

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

  1. $2\%$

  2. $5\%$

  3. $8\%$

  4. $10\%$

Show answer
Correct Option: A
Explanation:

Rate $= \displaystyle \left ( \frac{100 \times 300}{5000 \times 3} \right )$% = 2%

During a period of two years, a principal of Rs. $100$ amounts to Rs. $121$ at the annual compount rate of $r\%$. The value of $r$ will be

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

  1. $9$

  2. $10$

  3. $\displaystyle \frac{21}{2}$

  4. $11$

Show answer
Correct Option: B
Explanation:

Given, Sum (P) = Rs. 100,
Amount due (A) = Rs. 121
Time (n) = 2 years, Rate (r) = ?
We know $A = P \displaystyle \left ( 1 + \frac{r}{100} \right )$
$\therefore 121 = 100 \displaystyle \left ( 1 + \frac{r}{100} \right )^2$
or $\displaystyle \left ( 1 + \frac{r}{100} \right )^2 = \frac{121}{100}$
or $\displaystyle 1 + \frac{r}{100} = \frac{11}{10} = 1 + \frac{1}{10} = 1 + \frac{10}{100}$
$\therefore r = 10$%

Rajan lent Rs. $1200$ to Rakesh for $3$ years at a certain rate of interest and Rs. $1000$ to Mukesh for the same time at the same rate. If he gets Rs. $50$ more from Rakesh than from Mukesh, then the rate percent

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

  1. $ 8 \displaystyle \frac{1}{3}\%$ 

  2. $ 6 \displaystyle \frac{2}{3}\%$ 

  3. $ 10 \displaystyle \frac{1}{3}\%$ 

  4. $ 9 \displaystyle \frac{2}{3}\%$ 

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{1200 \times R \times 3}{100} - \frac{1000 \times R \times 3}{100} = 50$
or $6 R = 50$
or $R = \displaystyle 8 \frac{1}{3}$%