Question

Q.25 Rakesh invested 2000/-@ 5% per annum and 3000/- @ 4% per annum. After a certain time he found that
the difference between the interests in both investments was 780/-. Find the duration of the investment
PLEASE ANSWER THE QUESTION .



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Answer 1

$\sf{\orange{\boxed{\huge{Case\: 1}}}}$

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$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs. 2000
• Rate = 5%

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Interest = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Interest = \dfrac{P\times R\times T}{100}}}}}$

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$\sf: \implies\: {\bold{ Interest = \dfrac{2000\times 5\times 1}{100}}}$

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$\sf: \implies\: {\bold{ Interest = \dfrac{200\times 5\times 1}{10}}}$

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$\sf: \implies\: {\bold{ Interest = {20\times 5\times 1}}}$

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$\sf: \implies\: {\bold{ Interest = 100 t }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Interest in the 1st case is 100t

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$\sf{\orange{\boxed{\huge{Case\: 2}}}}$

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$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Principle = Rs. 3000
• Rate = 4%

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Interest = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Interest = \dfrac{P\times R\times T}{100}}}}}$

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$\sf: \implies\: {\bold{ Interest = \dfrac{3000\times 4\times 1}{100}}}$

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$\sf: \implies\: {\bold{ Interest = \dfrac{300\times 4\times 1}{10}}}$

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$\sf: \implies\: {\bold{ Interest = {30\times 4\times 1}}}$

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$\sf: \implies\: {\bold{ Interest = 120 t }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Interest for 2nd case is 120 t

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Now :-

Given that :-

• Interest ( 2nd case ) - Interest ( 1st case ) = 780

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To find :-

• Duration if the investment = ??

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Solution :-

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$: \implies\: \sf{\bold{ 120t - 100t = 780 }}$

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$: \implies\: \sf{\bold{ 20t = 780 }}$

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$: \implies\: \sf{\bold{ t = \dfrac{780}{20} }}$

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$: \implies\: \sf{\bold{ t = \dfrac{78}{2} }}$

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$: \implies\: \sf{\bold{ t = 39 years }}$

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Answers :-

• Duration of the investment = 39 years

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Answer 2

Answer:39 yrs

Step-by-step explanation:

First we have to find the interest in both cases.

Interest=P*R*T/100 [Case 1]                                         [Case 2}

            =2000*5*t/100                                              =3000*4*t/100

            =10000*t/100                                                =12000*t/100

            =By cancelling the zeros we get                =120t

            =100t

According to the question

120t-100t=780

20t=780

t=780/20

t=39 yrs