can someone clear how to factorize any question
Answers
Answer:
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
\begin{gathered}\boxed{ \rm{ \:SI \: = \: \frac{P \times r \times n}{100} \: }} \\ \end{gathered}
SI=
100
P×r×n
So, on substituting the values, we get
\begin{gathered}\rm \: SI_1 \: = \: \dfrac{20000 \times 10 \times 1}{100} \\ \end{gathered}
SI
1
=
100
20000×10×1
\begin{gathered}\rm\implies \:\boxed{ \rm{ \:SI_1 \: = \: Rs \: 2000 \: \: }} - - - (1) \\ \end{gathered}
⟹
SI
1
=Rs2000
−−−(1)
Case :- 2
Principal, P = Rs x
Rate of interest, r = 5 % per annum
Time, n = 1 year
So,
\begin{gathered}\rm \: SI_2 = \dfrac{x \times 5 \times 1}{100} \\ \end{gathered}
SI
2
=
100
x×5×1
\begin{gathered}\rm\implies \:\boxed{ \rm{ \:SI_2 \: = \: \frac{5x}{100} \: \: }} - - - (2) \\ \end{gathered}
⟹
SI
2
=
100
5x
−−−(2)
Case :- 3
Principal, P = Rs (20000 + x)
Rate of interest, r = 7 % per annum
Time, n = 1 year
So,
\begin{gathered}\rm \: SI_3 \: = \: \dfrac{(20000 + x) \times 7 \times 1}{100} \\ \end{gathered}
SI
3
=
100
(20000+x)×7×1
\begin{gathered}\rm\implies \:\boxed{ \rm{ \:SI_3 \: = \: \frac{140000 + 7x}{100} \: }} - - - (3)\\ \end{gathered}
⟹
SI
3
=
100
140000+7x
−−−(3)
Now, According to statement
\begin{gathered}\rm \: SI_3 = SI_1 + SI_2 \\ \end{gathered}
SI
3
=SI
1
+SI
2
On substituting the values from equation (1), (2) and (3), we get
\begin{gathered}\rm \: \dfrac{140000 + 7x}{100} = 2000 + \dfrac{5x}{100} \\ \end{gathered}
100
140000+7x
=2000+
100
5x
\begin{gathered}\rm \: \dfrac{140000 + 7x}{100} = \dfrac{200000 + 5x}{100} \\ \end{gathered}
100
140000+7x
=
100
200000+5x
\begin{gathered}\rm \: 140000 + 7x = 200000 + 5x \\ \end{gathered}
140000+7x=200000+5x
\begin{gathered}\rm \: 7x - 5x = 200000 - 140000 \\ \end{gathered}
7x−5x=200000−140000
\begin{gathered}\rm \: 2x = 60000 \\ \end{gathered}
2x=60000
\begin{gathered}\rm\implies \:x = 30000 \\ \end{gathered}
⟹x=30000
So,
\begin{gathered}\rm \:Total\:investment \: = \: 20000 +x \\ \end{gathered}
Totalinvestment=20000+x
\begin{gathered}\rm \:Total\:investment \: = \: 20000 +30000\\ \end{gathered}
Totalinvestment=20000+30000