Question

Q6: ₹10000 are deposited in a bank at the rate of 18% per annum amounted to
₹22,600 in few years. Find the time taken.​

Answer 1

QuestioN

• ₹10000 are deposited in a bank at the rate of 18% per annum amounted to

₹22,600 in few years. Find the time taken.

Given :

Here we are given that ₹ 10000 are deposited in a bank at the rate of 18% per annum amounted to

₹22,600 in few years and we are asked to find the time taken.

So, We are going to use two important formula for the above question i.e,

${\bullet \: \: {\boxed{\bf{Amount = Principle + Interest}}}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\ddagger \: \: {\boxed{\bf{SI = \dfrac{P \times R \times T}{100} }}}}$

Where,

◌ SI = Simple Interest

◌ P = Principle

◌ R = Rate of Interest

◌ T = No. of years

Word Explanation :

First we will going to find out the simple interest by substituting the given amount and principle value. There after, we will use simple Interest formula in order to find out the no. of years or time taken.

Now,

Answer ::

${\large{\frak{\pmb{\underline{ We\: know \:from \:given \:parameters }}}}}$

• P = Principle → ₹ 10,000

• Amount → ₹22,600

Now, putting in the formula :;

→→ Amount = Principle + Interest

✥ ₹22,600 = ₹ 10,000 + Interest

✥ ₹22,600 - ₹ 10,000 = Interest

✥ Interest = 12, 600

Now, For finding time taken

• →→ Simple Interest = P R T/ 100

• Interest → 12,600

• Principle → ₹ 10,000

• Rate of Interest → 18 %

So, Now

${\boxed{\dashrightarrow{\sf {12,600 = \dfrac{10, 000 \times 18 \times T}{ 100} }}}}$

${\boxed{\dashrightarrow{\sf {12,600 = \dfrac{18,0000 \times T}{ 100} }}}}$

Transposing, 100

${\boxed{\dashrightarrow{\sf {12,600 \times 100 = 18,0000 \times T }}}}$

${\boxed{\dashrightarrow{\sf {12,60000 = 18,0000 \times T }}}}$

Then, transposing ' 18,0000 '

${\boxed{\dashrightarrow{\sf {\dfrac{12,60000}{18,0000} = T }}}}$

${\boxed{\dashrightarrow{\sf {\dfrac{126{\cancel{0000}} }{18 {\cancel{0000}}} = T }}}}$

${\boxed{\dashrightarrow{\sf {T = {\dfrac{ {\cancel{126}^{ \: \: \: 7} } }{ {\cancel{18} }^{ \: \: \: 1} } }}}}}$

${\boxed{\bf{No. \: of \: years = {\red{7 \: years} }}}}$

Therefore,

Time taken is 7 years.

________________________

Answer 2

Answer:

$\pink\bigstar$ Given :-

• ↠ Principle = ₹10,000
• ↠ Amount = ₹22,600
• ↠ Rate of Interest = 18%

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ To Find :-

• ↠ Time

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Concept :-

⊙ Here we have given that the Principal is ₹10,000, Amonut is ₹22,600 and rate is 18 p.c.p.a. Here we need to find out the time.

⊙ So,Firstly we will find the interest and after finding interest we'll find the time by insert the values in the formula.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Using Formulae :-

$\begin{gathered}\quad\dag{\underline{\boxed{\bf{A= P + I}}}}\end{gathered}$

$\begin{gathered}\quad\dag{\underline{\boxed{\bf{T = \dfrac{S.I \times 100 }{P \times R} }}}}\end{gathered}$

Where

• A = Amount
• P = Principle
• I = Interest
• S.I = Simple Interest
• R = Rate of Interest
• T = Time

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Basic Terms :-

• ➽ Simple Interest = Simple interest is the method of calculating interest charged on the amount invested in a fixed deposit.
• ➽ Rate = An interest rate is the percentage of principal charged by the lender for the use of its money.
• ➽ Time = Time is duration (in months or years) in Simple Interest.
• ➽ Amount = The amount of something is how much there is, or how much you have, need, or get.
• ➽ Principal = Principal is the amount of money borrowed or invested.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Solution :-

⚘ Firstly, Finding the Interest :-

$\begin{gathered}\quad{\dashrightarrow{\sf{Amount= Principle + Interest}}}\end{gathered}$

• Substuting the values

$\begin{gathered}\quad{\dashrightarrow{\sf{22600= 1000 + Interest}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{ Interest = 22600 - 10000}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{ Interest = 12,600}}}\end{gathered}$

$\begin{gathered} \quad\bigstar\underline{\boxed{\textsf{\textbf{Interest = 12,600}}}}\end{gathered}$

∴ The interest is ₹12,600.

$\begin{gathered}\end{gathered}$

⚘ Now, Calculating the time :-

$\begin{gathered}\quad{\dashrightarrow{\sf{Time = \dfrac{S.I \times 100 }{P \times R} }}}\end{gathered}$

• Substuting the values

$\begin{gathered}\quad{\dashrightarrow{\sf{Time= \dfrac{12600\times 100 }{10000 \times 18}}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{Time= \dfrac{1260000 }{180000}}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{Time= \dfrac{126 \cancel{0000}}{18 \cancel{0000}}}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{Time= \dfrac{126 }{18}}}}\end{gathered}$

$\begin{gathered}\quad{\dashrightarrow{\sf{Time= \cancel\dfrac{126 }{18}}}}\end{gathered}$

$\begin{gathered}\quad{\bigstar{\underline{\boxed{\textsf{\textbf{Time= 7 years}}}}}}\end{gathered}$

∴ The time taken in interest is 7 years.

$\begin{gathered}\end{gathered}$

$\pink\bigstar$ Learn More :-

$\quad{ : \implies{\sf{ Simple \: Interest = \dfrac{P \times R \times T}{100}}}}$

$\quad{: \implies{\sf{Amount={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

$\quad{: \implies{\sf{Amount = Principle + Interest}}}$

$\quad{ : \implies{\sf{ Principle=Amount - Interest }}}$

$\quad{: \implies{\sf{Principle = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}$

$\quad{: \implies{\sf{Principle = \dfrac{Interest \times 100 }{Time \times Rate}}}}$

$\quad{: \implies{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}$

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