Question

Find the time when principal=1000,rate=8%per annum and Si=200

Answer 1

Answer:

Given :-

• Principal = Rs 1000, Rate of interest = 8% per annum and simple interest = Rs 200.

To Find :

• What is the time.

Formula :-

$\clubsuit$ Time Period Formula :

$\mapsto\sf\boxed{\bold{\pink{Time =\: \dfrac{S.I \times 100}{PR}}}}$

where,

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

Solution :-

Given :

$\bigstar\: \: \rm{\bold{Simple\: Interest\: (S.I) =\: Rs\: 200}}$

$\bigstar\: \: \rm{\bold{Principal\: (P) =\: Rs\: 1000}}$

$\bigstar\: \: \rm{\bold{Rate\: of\: Interest\: (R) =\: 8\%}}$

According to the question by using the formula we get,

$\longrightarrow \sf Time =\: \dfrac{200 \times 100}{1000 \times 8}$

$\longrightarrow \sf Time =\: \dfrac{20\cancel{000}}{8\cancel{000}}$

$\longrightarrow \sf Time =\: \dfrac{\cancel{20}}{\cancel{8}}$

$\longrightarrow \sf Time =\: \dfrac{\cancel{10}}{\cancel{4}}$

$\longrightarrow \sf Time =\: \dfrac{5}{2}$

$\longrightarrow \sf\bold{\red{Time =\: 2.5\: years}}$

$\therefore$ The time period is 2.5 years.

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Answer 2

$\bold{\bold{\Large{ \blue {\underline {\underline{Given \: Information:-}}}}}}$

• $\bf{ \hookrightarrow\: Principal \: is \: \: Rs.1000}$
• $\bf{ \hookrightarrow\: Rate \: is \: 8 \: percent}$
• $\bf{ \hookrightarrow \:Simple \: Interest \: is \: Rs.200 }$

‎

$\bold{\bold{ \Large {\blue {\underline {\underline{Need \: to \: calculate?}}}}}}$

• $\bf{ \hookrightarrow\: Time \: which \: had \: been \: taken}$

‎

$\bold{\bold{ \Large{\blue {\underline {\underline{Some \: Common \: Terms:-}}}}}}$

• The money borrowed is called the Principal
• The extra money paid for using lender's money is called the interest
• The total money, paid to the lender at the end of the specified period is called the amount.

‎

$\bold{\bold{\Large{ \blue {\underline {\underline{Step \: By \: Step \: Explaination:-}}}}}}$

_________

$\bf{\underbrace{ \underline{{Understanding \: the \: question \: and \: solving \: way}}}}$

»» First of all we would use the formula of calculating the simple interest that is Interest = Principal × Rate × Time / 100. But we aren't asked about to find out the simple interest as it is already given that is Rs.200 but we have to find out the time taken. Which would be calculated by reversing the sides of Simple Interest formula that is Time = Interest×100/Principal×Rate.

»» Further we would apply the values and solve it.

______

Calculations:-

• $\implies \bf{Time \: taken = \dfrac{100 \: \times \: Interest}{principal \: \times \: rate} }$

Applying the values:

• $\implies \bf{Time \: = \dfrac{100 \: \times \: 200}{1000 \: \times \: 8}}$

Cancelling terms:

• $\implies \bf{Time \: = \dfrac{ 1 \cancel{00} \: \times \: 200}{10 \cancel{00} \: \times \: 8}}$

• $\implies \bf{Time \: = \dfrac{ 1 \cancel{00} \: \times \: 200}{10 \cancel{00} \: \times \: 8}}$

• $\implies \bf{Time \: = \dfrac{200}{10\: \times \: 8}}$

• $\implies \bf{Time \: = \dfrac{200}{80}}$

• $\implies \bf{Time \: = \dfrac{2 0 \cancel0}{8 \cancel0}}$

• $\implies \bf{Time \: = \dfrac{2 0}{8}}$

Reducing to their lowest terms:

• $\implies \bf{Time \: = \dfrac{ \cancel{20}}{ \cancel{8}}}$

• $\implies \bf{Time \: = \dfrac{5}{2}}$

Conclusion:

• $\implies \bf{Time \: = 2.5 \: years}$

$\bold{\bold{\Large{ \blue {\underline {\underline{Answer:-}}}}}}$

• $\bf{Time \: which \: had \: been \: taken \: is \: 2.5 \: years}$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Note:–

• When interest is said, it always means Simple Interest.
• On the same sum and at the same rate of interest per annum, the interest of every year is same.