Question

Find the time when
Principal = Rs 9540, SI=Rs 1908.
and Rate = 6% p.a.​

Answer 1

Answer:

• Time period = 3 years and 4 months

Step-by-step explanation:

Given that:

• Principal = Rs 9540
• Simple Interest = Rs 1908
• Rate of Interest = 6% per annum

To Find:

• Time period.

Formula used:

• S.I. = (P × R × T)/100

Where,

• Simple Interest = S.I.
• Principal = P
• Rate of Interest = R
• Time period = T

Finding the time period:

⇒ S.I. = (P × R × T)/100

• Substituting the values.

⇒ 1908 = (9540 × 6 × T)/100

⇒ 9540 × 6 × T = 1908 × 100

⇒ T = (1908 × 100)/(9540 × 6)

⇒ T = 10/3

∴ Time period = 10/3 years

Converting 10/3 years into months:

• 1 year = 12 months
• 10/3 years = (12 × 10)/3 months
• 10/3 years = 40 months
• 10/3 years = 3 years and 4 months

Answer 2

Answer:

$\Large\underline\frak \red{Given}$

$\begin{gathered}\begin{gathered}\begin{gathered}&\bf\:Given - \begin{cases} &\sf{Principal = Rs. 9540} \\ &\sf{Simple \: Interest=Rs 1908.} \\& \sf{Rate = 6 \% \: p.a} \end{cases}\end{gathered}\end{gathered}\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\Large \underline\frak \red{To \: Find }$

$\begin{gathered}\begin{gathered}\begin{gathered}&\bf \:To \: find - \begin{cases} &\sf{Time } \end{cases}\end{gathered}\end{gathered}\end{gathered}$

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline \frak \red{Using \: Formula \: to \: find \: time }$

$: \implies\sf{S.I = \dfrac{P \times R \times T }{100}}$

$\small\begin{gathered}\begin{gathered}\begin{gathered}&\bf\:Where - \begin{cases} & \sf{S.I = Simple Interest} \\ & \sf{ P = Principal } \\ & \sf{R = Rate of Interest} \\& \sf{ T = Time} \end{cases}\end{gathered}\end{gathered}\end{gathered}$

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$\Large \underline\frak \red{Solution}$

✒ Finding Time by using S.I Formula.

So,

$: \implies \sf \pink{1908= \dfrac{ 9540\times6 \times T }{100}}$

$: \implies \sf \pink{9540\times6 \times T= {1908 \times 100}}$

$: \implies \sf \pink{T= \dfrac {1908 \times 100}{9540\times6}}$

$: \implies \sf \pink{T = \dfrac{\cancel{190800}} {\cancel{9540}\times 6} }$

$: \implies\sf \pink{T= \cancel \dfrac{20}{6} }$

$: \implies \sf \pink{T = \dfrac{10}{3}} \: \purple{years}$

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✒ Coverting 10/3 into moths

As we know that 1 year = 12 months

So,

$: \implies \sf \purple{\dfrac{10}{\cancel{3} } \times \cancel{ 12}}$

$: \implies \sf \purple{10 \times 4}$

$\implies \sf {\purple{40 }}\: {\pink{months}}$

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✒ Converting 40 months into years

we know that 12 = 1 years

So,

$: \implies \sf \purple{\dfrac{40}{12}}$

$: \implies \textsf \purple{3 \: years \: 4 months}$

$\large\underline {\boxed{\frak \pink{Time} = \sf\purple {3 \:years \: 4 \: months}}}$

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$\Large \underline\frak \red{Therefore}$

↝ The time period is 3 years 4 months.