Question

in what time will the simple interest on a certain sum be third-fourth of the principal 6% per annum​ .​

Answer 1

Step - by - step explanation:

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☯ Let the principal amount be Rs. 100

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${\underline{\sf{\bigstar\; According\;to\; Question\;:}}}$

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Simple Interest should be $\bf {}^{\text3}\!/{}_{\text{4}}th$ of the principal.

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Therefore,

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$\sf Simple\; Interest = \cancel{100} \times \dfrac{1}{ \cancel{4}}$

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$\sf Simple\; Interest = {\bf{\red{Rs.\;75}}}$

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So,

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$\bf We\;have = \begin{cases} & \text{Principal = Rs.\; 100} \\ & \text{Rate = 6\% } \\ & \text{Simple\; Interest = Rs.\;75} \end{cases}$

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Now, We have to find Time,

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We know that,

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$\star\;{\boxed{\sf{\purple{Simple\; Interest = \dfrac{P \times R \times T}{100}}}}}$

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$\;\;\;\;\small\sf \underline{Putting\;Values\;:}$

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$:\implies\sf 75 = \dfrac{100 \times 6 \times T}{100}$

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$:\implies\sf 75 = \dfrac{ \cancel{100} \times 6 \times T}{ \cancel{100}}$

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$:\implies\sf 75 = 6 \times T$

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$:\implies\sf T = \cancel{ \dfrac{75}{6}}$

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$:\implies{\underline{\boxed{\sf{\pink{T = {}^{\text25}\!/{}_{\text{2}}\;or\;12\;years\;and\;6\;months}}}}}\;\bigstar$

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$\therefore$ Hence, In 12 years and 6 months the simple interest on a certain sum be third-fourth of the principal 6% per annum.