Question

trouble fell on us.What was the trouble?How was it solved Answer the following questions in about 80 word
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Answer 1

Answer:

$\large\underline{\sf{Solution-}}$

Given that,

A man invested Rs. 20000 at 10% per annum at simple interest.

Another amount at 5% per annum at simple interest.

At the end of the year he got 7% interest on the entire investment.

Let assume that

The amount invested at the rate of 5 % per annum be Rs x

Case :- 1

Principal, P = Rs 20000

Rate of interest, r = 10 % per annum

Time, n = 1 year

We know,

Simple interest (SI) received on a certain sum of money of Rs P invested at the rate of r % per annum for n years is given by

$\boxed{ \rm{ \:SI \: = \: \frac{P \times r \times n}{100} \: }}$

So, on substituting the values, we get

$\rm \: SI_1 \: = \: \dfrac{20000 \times 10 \times 1}{100}$

$\rm\implies \:\boxed{ \rm{ \:SI_1 \: = \: Rs \: 2000 \: \: }} - - - (1)$

Case :- 2

Principal, P = Rs x

Rate of interest, r = 5 % per annum

Time, n = 1 year

So,

$\rm \: SI_2 = \dfrac{x \times 5 \times 1}{100}$

$\rm\implies \:\boxed{ \rm{ \:SI_2 \: = \: \frac{5x}{100} \: \: }} - - - (2)$

Case :- 3

Principal, P = Rs (20000 + x)

Rate of interest, r = 7 % per annum

Time, n = 1 year

So,

$\rm \: SI_3 \: = \: \dfrac{(20000 + x) \times 7 \times 1}{100}$

$\rm\implies \:\boxed{ \rm{ \:SI_3 \: = \: \frac{140000 + 7x}{100} \: }} - - - (3)$

Now, According to statement

$\rm \: SI_3 = SI_1 + SI_2$

On substituting the values from equation (1), (2) and (3), we get

$\rm \: \dfrac{140000 + 7x}{100} = 2000 + \dfrac{5x}{100}$

$\rm \: \dfrac{140000 + 7x}{100} = \dfrac{200000 + 5x}{100}$

$\rm \: 140000 + 7x = 200000 + 5x$

$\rm \: 7x - 5x = 200000 - 140000$

$\rm \: 2x = 60000$

$\rm\implies \:x = 30000$

So,

$\rm \:Total\:investment \: = \: 20000 +x$

$\rm \:Total\:investment \: = \: 20000 +30000$

$\rm\implies \:\boxed{ \bf{ \:Total\:investment \: = \: Rs \: 50000 \: }}$

$\rm\implies \:$Option (d) is correct

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{P = \dfrac{SI \times 100}{r \times n} }\\ \\ \bigstar \: \bf{r = \dfrac{SI \times 100}{P \times n} }\\ \\ \bigstar \: \bf{n = \dfrac{SI \times 100}{P \times r} }\\ \\ \bigstar \: \bf{Amount = P\bigg(\dfrac{100 + rn}{100} \bigg) }\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

The people of the kingdom were confused as to how their king and the minister were dead instead of the Guru and the disciple. The people were not able to see through the plan which was executed by the Guru against their king and minister.