Question

In how many years, a sum of Rs.500 at 5% per annum will amount to Rs.600?

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Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• A sum of Rs.500 at 5% per annum will amount to Rs.600

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• How many years?

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Amount = Rs. 600

• Principal Amount = Rs. 500

• Rate of interest = 5%

We know that,

$\boxed{\pink{\sf S.I \: = \: A \: - \: P}}$

Substituting the values,

• S.I = Rs. 600 - Rs. 500

• S.I = Rs. 100

We know that,

$\boxed{\pink{\sf S.I \: = \: \dfrac{P \: * \: T \: * \: R}{100}}}$

Substituting the values,

• $\sf 100 \: = \: \dfrac{500 \: * \: T \: * \: 5}{100}$

• $\sf 100 \: * \: 100 \: = \: 500 \: * \: T \: * \: 5$

• $\sf 10000 \: = \: 2500 \: * \: T$

• $\sf \dfrac{10000}{2500} \: = \: T$

• $\sf \dfrac{100\cancel{00}}{25\cancel{00}} \: = \: T$

• $\sf \dfrac{100}{25} \: = \: T$

• $\sf \dfrac{\cancel{100}}{\cancel{25}} \: = \: T$

• $\sf T \: = \: 4$

Therefore,

• It takes 4 years for a sum of Rs.500 at 5% per annum to become Rs.600.

$\Large{\bf{\purple{\mathfrak{\dag{\underline{\underline{Formulas \: Used:-}}}}}}}$

$\blue{\sf S.I \: = \: A \: - \: P}$

• where,

• S.I = Simple Interest

• A = Amount

• P = Principal Amount

$\blue{\sf S.I \: = \: \dfrac{P \: * \: T \: * \: R}{100}}$

• where,

• S.I is Simple Interest

• P is Principal Amount

• T is Time

• R is Rate of interest

Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf \: Rate = 5 \: \% \: per \: annum$

$\sf \: Principal = Rs. \: 500$

$\sf \: Amount = Rs. \: 600$

$\bf \: \underline{To \: Find}:$ ↴

$\sf \: We \: have \: to \: find \: the \: time.$

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

$\sf \: First \: of \: all \: we \: have \: to \: find \: the \: Simple \: Interest.$

$\sf \implies \: S.I = Amount - Principal$

$\sf\implies \: S.I = 600 - 500$

$\sf \implies \: S.I = 100$

$\bf \: Now ,$

$\sf \: We \: will \: find \: the \: time,$

$\sf\longrightarrow \: 100 = \dfrac { P \times R \times T } { 100 }$

$\sf \: Where,$

$\sf \bull \longmapsto \: P = Principal$

$\sf \: \bull \longmapsto \: R = Rate$

$\sf \bull \longmapsto \: T = Time$

$\sf \: \underline{Putting \: the \: values},$

$\sf\implies \: 100 = \dfrac { 500 \times 5 \times T } { 100 }$

$\sf \: Simplifying \: the \: above \: expression,$

$\sf\implies \: 100 = \dfrac { 2500 \times T } { 100 }$

$\sf \: Cutting \: of \: Zero's,$

$\sf\implies \: 100 = \dfrac { 25\!\!\!\not0\!\!\!\not0 \times T } { 1\!\!\!\not0\!\!\!\not0 }$

$\sf\implies \: 100 = \dfrac { 25 \times T } { 1 }$

$\sf\implies \: T = \dfrac{100}{25}$

$\sf\implies \: T = 4$

$\underline{ \boxed{ \sf\pink{Hence, time = 4 \: Years. }}}$