In the given figure , AB and CD are two chords of a circle with centre
O and AB = 16 cm , CD = 12 cm and AB ║ CD . If OP ⊥ AB , OQ ⊥
AB and OQ = 6 cm . Find the length of OP.
Answers
Answer:
\large\underline{\sf{Solution-}}
Solution−
Given that,
Rs. 25,000 invested for 2 years at compound interest, if the rates for the successive years be 4 and 5 per cent per year.
So, we have
Principal, P = Rs 25000
Rate of interest, r = 4 % per annum compounded annually.
Time, n = 1 year
Rate of interest, R = 5 % per annum compounded annually
Time, m = 1 year
We know,
Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years and R % per annum compounded annually for next m years is given by
\begin{gathered}\boxed{\sf{ \:Amount = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} {\bigg[1 + \dfrac{R}{100} \bigg]}^{m} \: }} \\ \end{gathered}
Amount=P[1+
100
r
]
n
[1+
100
R
]
m
So, on substituting the values, we get
\begin{gathered}\rm \: Amount = 25000 {\bigg[1 + \dfrac{4}{100} \bigg]}^{1} {\bigg[1 + \dfrac{5}{100} \bigg]}^{1} \\ \end{gathered}
Amount=25000[1+
100
4
]
1
[1+
100
5
]
1
\begin{gathered}\rm \: Amount = 25000 {\bigg[1 + \dfrac{1}{25} \bigg]} {\bigg[1 + \dfrac{1}{20} \bigg]} \\ \end{gathered}
Amount=25000[1+
25
1
][1+
20
1
]
\begin{gathered}\rm \: Amount = 25000 {\bigg[ \dfrac{25 + 1}{25} \bigg]} {\bigg[ \dfrac{20 + 1}{20} \bigg]} \\ \end{gathered}
Amount=25000[
25
25+1
][
20
20+1
]
\begin{gathered}\rm \: Amount = 25000 {\bigg[ \dfrac{26}{25} \bigg]} {\bigg[ \dfrac{21}{20} \bigg]} \\ \end{gathered}
Amount=25000[
25
26
][
20
21
]
\begin{gathered}\rm\implies \:Amount = Rs \: 27300 \\ \end{gathered}
⟹Amount=Rs27300
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Additional Information :-
1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by
\begin{gathered}\boxed{\sf{ \:Amount = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: }} \\ \end{gathered}
Amount=P[1+
100
r
]
n
2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by
\begin{gathered}\boxed{\sf{ \:Amount = P {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }} \\ \end{gathered}
Amount=P[1+
200
r
]
2n
3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by
\begin{gathered}\boxed{\sf{ \:Amount = P {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: }} \\ \end{gathered}
Amount=P[1+
400
4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by
\begin{gathered}\boxed{\sf{ \:Amount = P {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: }} \\ \end{gathered}
Amount=P[1+
1200
r
]
12n