Question

if the simple interest on a certain sum of money for 2 years be 1/3 of the Sum , find the rate of interest per annum?

Please solve it with proper and simple explanation​

Answer 1

Step-by-step explanation:

Given :-

The simple interest on a certain sum of money for 2 years is 1/3rd of the sum.

To find :-

The rate of interest per annum .

Solution :-

Let the sum be Rs. X

Let the rate of interest per annum be R%

Time (T) = 2 years

Simple Interest (S.I) = 1/3rd of the sum

=> S.I. = 1/3 of X

=> S.I. = (1/3)×X

=> S.I. = (1×X)/3

=> S.I. = X/3

Therefore, Simple Interest = Rs. X/3

We know that

Simple Interest = PTR/100

=> X/3 = (X×2×R)/100

=> X/3 = 2RX/100

=> X/3 = RX/50

On applying cross multiplication then

=> RX × 3 = 50×X

=> 3RX = 50X

=> R = 50X/3X

=> R = 50/3 %

=> R = 16 2/3 %

Therefore, Rate of Interest = 50/3% or

16 2/3%

Answer :-

The rate of interest per annum is 50/3% or 16 2/3%

Check:-

Sum = Rs. X

Time = 2 years

Rate of interest = 50/3 %

Simple Interest = PTR/100

=> S.I. = (X×2×50)/(100×3)

=> S.I. = 100X/300

=> S I. = X/3

=> S.I. = 1/3 of X

Therefore, Simple Interest is 1/3rd of the sum .

Verified the given relations in the given problem.

Used formulae:-

→ Simple Interest = PTR/100

• P = Principal
• T = Time
• R = Rate of Interest

Answer 2

Question

If the simple interest on a certain sum of money for 2 years be 1/3 of the Sum , find the rate of interest per annum?

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Required Answer

${\pink{\dashrightarrow}{\qquad{\sf{R = 16.66... \: \:\% \: p.a }}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Information provided with us -

➡ Time = 2 years

➡ Simple Interest = 1/3 years

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

What we have to Find out ;

➡ Rate of interest per annum (R)

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Consider :

➡ Assume that the Principal be x and S.I = x/3

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

So we have :

$\bigstar{\underline{\boxed{\red{\sf{Principle = x}}}}}$

$\bigstar{\underline{\boxed{\pink{\sf{Simple \: Interest = \dfrac{x}{3} }}}}}$

$\bigstar{\underline{\boxed{\red{\sf{Time = 2 \: years }}}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Formula used :

$\bigstar{\underline{\boxed{\green{\sf{R = \bigg(\dfrac{S.I \times 100}{P \times \: T }\bigg)}}}}}$

${\large{\underline{\pmb{\frak{Where}}}}}$

➡ T = Time

➡ P=Principal

➡ R=Rate

➡ S.I = Simple Interest

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

$\qquad{\Large{\underline{\underline{\blue{\bf{Solution}}}}}}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\pmb{\frak{Calculating\:Rate}}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{R = \bigg(\dfrac{ S.I \times 100}{P \times T}\bigg)}}}}$

➡ By putting the values in given formula

${\pink{\dashrightarrow }{\qquad{\sf{R = \bigg(\dfrac{ \dfrac{x}{3} \times 100}{x \times 2}\bigg)}}}}$

➡ Here x and x get cancelled out and By doing further calculation we get

${\pink{\dashrightarrow}{\qquad{\sf{R = \bigg(\dfrac{ 100 }{3 \times 2}\bigg)}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{R = \bigg(\dfrac{ 100 }{6}\bigg)}}}}$

${\pink{\dashrightarrow}{\qquad{\sf{R = 16.66... \: \:\% \: p.a }}}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

${\large{\underline{\pmb{\frak{Therefore}}}}}$

➡The required rate of interest is 16.66 % p.a

$\begin{gathered} \\ {\underline{\rule{200pt}{6pt}}} \end{gathered}$