Question

a man invested rupees 25000 at a certain rate of CI per annum to get rupees 29160 in 2 years find the rate of interest​

Answer 1

S O L U T I O N :

$\bf{\large{\underline{\bf{Given\::}}}}}$

• Principal, (P) = Rs.25000
• Amount, (A) = Rs.29160
• Time, (n) = 2 years

$\bf{\large{\underline{\bf{To\:find\::}}}}}$

The rate of interest.

$\bf{\large{\underline{\bf{Explanation\::}}}}}$

We know that formula of the compounded annually :

$\boxed{\bf{A=P\bigg(1+\frac{R}{100} \bigg)^{n} }}}}$

A/q

$\longrightarrow\tt{29160=25000\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\tt{\dfrac{2916\cancel{0}}{2500\cancel{0}} =\bigg(1+\dfrac{R}{100} \bigg)^{2}} \\\\\\\longrightarrow\tt{\dfrac{2916}{2500} =\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\tt{\sqrt{\dfrac{2916}{2500} } =1+\dfrac{R}{100} }\\\\\\\longrightarrow\tt{\dfrac{54}{50} =1+\dfrac{R}{100} }\\\\\\\longrightarrow\tt{\dfrac{54}{50} -1=\dfrac{R}{100}}\\\\\\\longrightarrow\tt{\dfrac{54-50}{50} =\dfrac{R}{100}}$

$\longrightarrow\tt{\dfrac{4}{50} =\dfrac{R}{100} }\\\\\\\longrightarrow\tt{50R=400\:\:\:\underbrace{\sf{Cross-multiplication}}}\\\\\\\longrightarrow\tt{R=\cancel{\dfrac{400}{50} }}\\\\\\\longrightarrow\bf{R=8\%}$

Thus;

The rate of the interest will be 8% p.a .

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Principal = 25000Rs
• Amount = 29160
• Time = 2 years

${\bf{\blue{\underline{Given:}}}}$

• Rate of interest =?

${\bf{\blue{\underline{Formula\:Used:}}}}$

$\dagger \: \: \boxed{\sf{ A = P \bigg(1 + \frac{R}{100} \bigg) ^{T} }}$

${\bf{\blue{\underline{Now:}}}}$

$: \implies{\sf{ 29160 = 25000 \bigg(1 + \frac{R}{10} \bigg) ^{2} }}$

$: \implies{\sf{ \frac{29160}{25000} = \bigg(1 + \frac{R}{10} \bigg) ^{2} }}$

$: \implies{\sf{ \frac{2916}{2500} = \bigg(1 + \frac{R}{10} \bigg) ^{2} }}$

$: \implies{\sf{ \bigg( \frac{54}{50} \bigg) ^{2} = \bigg(1 + \frac{R}{10} \bigg) ^{2} }}$

If the exponent are equal bases will also be equal,

$: \implies{\sf{ \frac{54}{50} = 1 + \frac{R}{100} }}$

$: \implies{\sf{ \frac{R}{100} = \frac{54}{50} - 1}}$

$: \implies{\sf{ \frac{R}{100} = \frac{54 - 50}{50} }}$

$: \implies{\sf{ \frac{R}{100} = \frac{4}{50} }}$

$: \implies{\sf{ R \times 50} = 4\times 100 }$

$: \implies{\sf{ R \times 50} = 400 }$

$: \implies{\sf{ R } = \frac{400}{50} }$

$: \implies{\sf{ R } = 8\% }$

$\dagger \: \boxed{\sf{ \purple{Rate \: of \: interset \: = 8\% }}}$