Tag: maths

Questions Related to maths

The profit of a company (whose capital is divided into 25, 000 shares of Rs. 10 each) for the last three years are: Rs. 50, 000; Rs. 60, 000 and Rs. 40, 000. The fair return on investment is taken at 10% p.a. The value of company's share will be __________.

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. 10

  2. Rs. 20

  3. Rs. 30

  4. Rs. 40

Show answer
Correct Option: B

Ajay and Anil start a business in partnership. Anil invested $Rs.300$ more that Ajay for half the number of months that Ajay did. If, out of the total profit of $Rs.375$ of the one year, Ajay got $Rs.25$ more than Anil, what was the investment made by Anil?  

investement and financial planning banking compound interest comparing quantity maths

  1. $Rs.800$

  2. $Rs.350$

  3. $Rs.700$

  4. $Rs.400$

Show answer
Correct Option: B

Mr. Dua invested money in two schemes P and Q offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a respectively. if the total amount of interest accrued two schemes together in two years was Rs 4818.30 and the total amount invested was Rs 27, 000, what was the amount invested in Scheme P?

investement and financial planning banking compound interest comparing quantity maths

  1. Rs 12, 000

  2. Rs 13,500

  3. Rs 15, 000

  4. None of these

Show answer
Correct Option: A
Explanation:

Let p invested Rs x Then q invested Rs $(27000-x)$
$\therefore x(1+\dfrac{8}{100})^{2}-1+(27000-x)(1+\dfrac{9}{100})^{2}-1=4818.30$
$\Rightarrow (x\times \dfrac{104}{625})+\dfrac{1881(27000-x)}{10000}= \dfrac{481830}{100}$
$\Rightarrow 1664x+1881(27000-x)=48183000$
$\Rightarrow (1881x-1664x)=50787000-48183000$
 Or $217x=2604000$
  Or $x=12000 Rs$

A family made a down payment of $75 and borrowed a set of encyclopedias that cost $400. The balance with interest was paid in 23 monthly payments of $16 each and a final payment of $9. What was the per cent of interest to the borrowed sum?

investement and financial planning banking compound interest comparing quantity maths

  1. 12 %

  2. 14 %

  3. 16 %

  4. 18 %

Show answer
Correct Option: C
Explanation:

Total cost =$ 400
Down payment=$ 75
Remaining amount=$400-75=$ 325$
Balanced paid in 24 months=$23 \times 16+9=$ 377$
Difference=$377-325=$52$
The per cent of interest to the borrowed sum=$\frac{52}{325}\times 100=16$


A $500 investment and a $1,500 investment have a combined yearly return of 8.5 per cent of the total of the two investments. If $500 investment has a yearly return of 7 per cent, what per cent yearly return does the $1,500 investment have?

investement and financial planning banking compound interest comparing quantity maths

  1. $9$

  2. $10$

  3. $11$

  4. $11\displaystyle \frac{1}{9}$

Show answer
Correct Option: A
Explanation:

Total investment by A=$500+1500=2000$
Yearly return =8.5 % of 2000
$\Rightarrow \frac{8.5}{100}\times2000=170$
Yearly return of 500=7% of 500
$\Rightarrow \frac{7}{100}\times500=35$
Let yearly return of 1500 is x
Yearly return=x% of 1500
$\Rightarrow \frac{x}{100}\times 1500=15x$
Then according to the question
$\Rightarrow 35+15x=170$
$\Rightarrow 15x=170-35$
$\Rightarrow 15x=135$
$\Rightarrow x=\frac{135}{15}=9$
                     

$A$ started a business with a capital of $Rs.10000$. Four month later, $B$ joined him and $2$ more moth letter , $C$ joined them in the partnership. If at the end of the year, all of them got an equal shares of profit, what was $C's$ investment? 

investement and financial planning banking compound interest comparing quantity maths

  1. $Rs.15000$

  2. $Rs.20000$

  3. $Rs.18000$

  4. $Rs.22000$

Show answer
Correct Option: A

A person pays $ $400$ every year as loan installments to a bank. If every year bank increases the installment amount by $10$%, the find the total amount he pays in installments in $4$ years. 

investement and financial planning banking compound interest comparing quantity maths

  1. $ $1324 $

  2. $ $1456.4 $

  3. $ $1856.4 $

  4. $ $884 $

Show answer
Correct Option: C
Explanation:

Given  person pays $400$ every as loan installments to bank

And every year bank increases installments $10\%$ every year 
Then after one year installments $=$ $400\times \dfrac{110}{100}=$440$
And after two year installments$440\times \dfrac{110}{100}=$484$
And after three year installments$484\times \dfrac{110}{100}=$532.40$
Then person paid installments in $4$ years $=$ $400+440+484+532.40=1856.40$

A man borrows Rs. $200$ at $ 5$% compound interest. At the end of each year he pays back Rs. $50$. At the end of $4 $ years he owes

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. $27.59$

  2. Rs. $28.10$

  3. Rs. $27.81$

  4. Rs. $28.14$

Show answer
Correct Option: A
Explanation:

Amount of one year

$\displaystyle=200\left[1+\frac{5}{100}\right]$

$\displaystyle=200\times\frac{21}{20}=210$

$\therefore$ At the end of year he pays back Rs. 50. So the principal for the second year is Rs. 160.
$\therefore$ Amount of Second year

$\displaystyle=160\left[1+\frac{5}{100}\right]$

$\displaystyle=160\times\frac{21}{20}=168$

$\therefore$ At the end of year he pays back Rs. 50. 
So rest amount = 168 -50 = Rs. 118.
This amount is principal amount for third year.
$\therefore$ Amount of third year

$\displaystyle=118\left[1+\frac{5}{100}\right]$

$\displaystyle=118\times\frac{21}{20}=123.90$

At the end of years he pays back Rs. 50.
So rest amount
$=123.90-50=Rs. 73.90$
This amount is principal for fourth year.
$\therefore$ Amount of fourth year

$\displaystyle=73.90\left[1+\frac{5}{100}\right]$

$\displaystyle=73.90\times\frac{21}{20}=77.59$

At the end of year he pays back Rs. 50.
So rest amount
$=77.595-50=Rs. 27.59$
$\therefore$ At the end of fourth year he owes Rs. 27.59.

Lakshman borrowed Rs. $20$ lakhs as housing loan from ICICI at $10\%$ p.a to be repaid in $10$ years. if the EMI is Rs. $2500$ per lakh, find how much he pays as interest in the first month. Find also he principal repaid then.

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. $33333.34$

  2. Rs. $33344.64$

  3. Rs. $36543.45$

  4. Rs. $54600$

Show answer
Correct Option: A
Explanation:

Interest at $10\%$ for the first month for Rs. $20$ lakhs $=$ $2000000 \times \dfrac{1}{12}\times \dfrac{10}{100}=16666.66$
EMI for one month, for $20$ lakhs $= 2500 \times  20 =$ Rs. $50000$
Hence principal repaid $=$ Rs. $50000 - 16666.66 =$ Rs. $33333.34$

A sum of Rs $550$ was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be $20\%$ compounded annually, then the amount of each instalment will be

investement and financial planning banking compound interest comparing quantity maths

  1. Rs $360$

  2. Rs $350$

  3. Rs $340$

  4. Rs $300$

Show answer
Correct Option: B
Explanation:
Let $x$ be each installment
After paying the first installement $x$
the remaininng principle is $ 550\times1.2-x$
This then compounded yearly should be equal to the second installment
$\left(550\times1.2-x\right)\times 1.2= x$
$ 550\times 1.2^2-x\times 1.2 = x$
$792=2.2\times x$
$x=360$
Thus eachn installemnt should be $Rs.360$