Quiz-1

P = 8000,

CI = 9261,

R = 5% per annum

⇒ 9261 = 8000( 1+\frac{5}{100})^{n}


⇒ \frac{9262}{8000} = (\frac{21}{20})^{n}
⇒ (\frac{21}{20})^{3} =(\frac{21}{20})^{n}
⇒ n= 3

Let the initial amount be 100.
Using the simple unitary method,
100 becomes 200 → 4 yrs
200 becomes 400 → 4 yrs
400 becomes 800 → 4 yrs

∴ Total years = 12

We have, Decrease in value =  6\frac{1}{4}% =\frac{25}{4} % = 0.0625
∴ Remaining of value = 1- 0.0625 = 0.9375

Let the value at the beginning of the first year = Rs. x
⇒ x × 0.9375 × 0.9375 × 0.9375 = 21093
⇒ x = Rs. 25599.09

1525-1300= 225 for 1.5 yrs (3.5-2)
So, for 1 yr = \frac{225}{1.5}= 150
then for 2 yrs, the interest = 150+150=300
Then principal 1300-300=1000.

Rate  = \frac{SI\times 100}{P\times T}

Rate  = \frac{300\times 100}{1000\times 2}  = 15 %

We know, \frac{[P(1+\frac{r}{100})^{2}]}{[P(1+\frac{r\times 1}{100})]}=\frac{6}{5}
⇒ 1+\frac{r}{100}=\frac{6}{5}
⇒ \frac{r}{100}=\frac{1}{5}
⇒ r=20%

Let the principal be Rs x.
Then the SI =\frac{4x}{25}
Rate of interest = Time
⇒ r= \frac{100\times \frac{4}{25}x}{x\times r}
⇒ r² =\frac{400}{25}

⇒ r=\frac{20}{5} = 4

Hence, rate of interest = 4%

It is compounded half yearly

so Rate = \frac{4}{2}=2

value of t= 2 x 2 = 4

CI = Principal (1 +\frac{r}{100})^{t} - Principal

Its calculated half yearly so rate will get half and time will get doubled
= 20000 (1 + \frac{2}{100})^{4} - 20000
= 20000 (\frac{51}{50})^{4} - 20000
= 20000 \times  \frac{51}{50} \times  \frac{51}{50} \times  \frac{51}{50} \times \frac{51}{50} - 20000
= 21648.64 - 20000

= Rs. 1648.64

"Interest for 1 year is the same whether it's simple interest or the compound interest.

Now interest of third year = 8000 - 7000 = 1000; means principal for this interest is 7000 if compound interest is taken
If 7000 is the principal, interest = 1000
if 100 is the principal, interest =(\frac{1000}{7000}) \times  100 = (\frac{100}{7}) %
When a thing increases for two successive times the overall increase on initial amount = a + b + \frac{(a\times b)}{100}
Therefore, overall interest for two years = \frac{100}{7} + \frac{100}{7} + \frac{[(\frac{100}{7})\times (\frac{100}{7})]}{100} = \frac{1500}{49} = 30.61
Therefore amount after 2 years = 100 + \frac{1500}{49} = \frac{6400}{49}
If \frac{6400}{49} is the amount, principal =100
if 7000 is the amount, principal =\frac{100}{\left (\frac{6400}{49} \right )}\times 7000 = 5359.375

So sum = Rs. 5359.375

Amitabh's share / Jaya's share

[ 1+ 5/100]^11 / [ 1 + 5/100]^9

[ 21 / 100]^11 / [ 21 / 100]^9

[ 21 / 100]^2

441/400

Then, Amitabh’s share,
= (441/841)*5887
= 2596167 / 841
= 3087

Let the amount Amir khan invested at the rate of 10% = Rs x
then the amount invested at 15% = Rs (50,000 - x)
Time = 1yr
Income from 10% rate = 10% of x = \frac{x}{10}
Income from 15% rate = 15% of (50,000 - x) = \frac{(150,000 - 3x)}{20}
Acc to ques, [\frac{x}{10}] + [\frac{(150,000 - 3x)}{20}] = 7000
⇒ 150000 - x = 140000
⇒ x = 10,000.

Therefore, he has invested Rs 10,000 at 10% and Rs 40,000 at 15%.