in what time will the simple interest on a certain sum be third-fourth

1.	in what time will the simple interest on a certain sum be third-fourth of the principal 6% per annum .
Answer» Step - by - step explanation: ⠀⠀⠀⠀⠀⠀⠀ ☯ Let the principal amount be Rs. 100 ⠀⠀⠀⠀⠀⠀⠀ ${\underline{\sf{\bigstar\; According\;to\; Question\;:}}}$ ⠀⠀⠀⠀⠀⠀⠀ Simple Interest should be $\bf {}^{\text3}\!/{}_{\text{4}}th$ of the principal. ⠀⠀⠀⠀⠀⠀⠀ Therefore, ⠀⠀⠀⠀⠀⠀⠀ $\sf Simple\; Interest = \cancel{100} \times \dfrac{1}{ \cancel{4}}$ ⠀⠀⠀⠀⠀⠀⠀ $\sf Simple\; Interest = {\bf{\red{Rs.\;75}}}$ ━━━━━━━━━━━━━━━ ⠀⠀⠀⠀⠀⠀⠀ So, ⠀⠀⠀⠀⠀⠀⠀ $\bf We\;have = \begin{cases} & \text{Principal = Rs.\; 100} \\ & \text{Rate = 6\% } \\ & \text{Simple\; Interest = Rs.\;75} \end{cases}$ ⠀⠀⠀⠀⠀⠀⠀ Now, We have to find TIME, ⠀⠀⠀⠀⠀⠀⠀ We know that, ⠀⠀⠀⠀⠀⠀⠀ $\star\;{\boxed{\sf{\purple{Simple\; Interest = \dfrac{P \times R \times T}{100}}}}}$ ⠀⠀⠀⠀⠀⠀⠀ $\;\;\;\;\small\sf \underline{Putting\;Values\;:}$ ⠀⠀⠀⠀⠀⠀⠀ $:\implies\sf 75 = \dfrac{100 \times 6 \times T}{100}$ ⠀⠀⠀⠀⠀⠀⠀ $:\implies\sf 75 = \dfrac{ \cancel{100} \times 6 \times T}{ \cancel{100}}$ ⠀⠀⠀⠀⠀⠀⠀ $:\implies\sf 75 = 6 \times T$ ⠀⠀⠀⠀⠀⠀⠀ $:\implies\sf T = \cancel{ \dfrac{75}{6}}$ ⠀⠀⠀⠀⠀⠀⠀ $:\implies{\underline{\boxed{\sf{\pink{T = {}^{\text25}\!/{}_{\text{2}}\;or\;12\;years\;and\;6\;months}}}}}\;\bigstar$ ⠀⠀⠀⠀⠀⠀⠀ $\therefore$ Hence, In 12 years and 6 months the simple interest on a CERTAIN SUM be third-fourth of the principal 6% PER annum.