In what time will the interest on a certain Sumof money at 6 \% be 5/8 of itself?

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Given:

S.I = 4P/5

Rate(R) = 20%

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Calculation:

Let the time be x years and the sum of money be Rs. P

Simple Interest = (Principal × Rate × Time)/100

⇒ Simple Interest = (P × 20 × x)/100

⇒ (4/5) × P = (P × 20 × x)/100

⇒ x = 4

∴ The required time is 4 years.

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Answer

Verified

Hint: Simple interest or interest figured on the principal amount only, for the duration of the loan.
The rate % (percentage) per annum on the principal amount and the duration of the loan are the factors for calculating simple interest.Complete step by step solution:
Step 1
Let the time period = t years
Let the principle amount = P rupees
Given:
Rate % per annum on principal amount P = 6%

Step 2
Condition for interest stated in question:
Interest amount is $\dfrac{5}{8}$ times of principal amount, P.
$ \Rightarrow {\rm{I}} = \dfrac{5}{8}{\rm{P}}$ …… (1)

Step 3
Here, I in terms of P, P and r are given, only one unknown time period, t
Therefore,
Using simple interest formula, where
                                                              ${\rm{I}} = \dfrac{{\Pr t}}{{100}}$
$\begin{array}{l}
 \Rightarrow {\rm{ }}\dfrac{5}{8}P = \dfrac{{P \times 6 \times t}}{{100}}\\
 \Rightarrow {\rm{ }}\dfrac{5}{8}{P} = \dfrac{{{P} \times 6 \times t}}{{100}}\\
 \Rightarrow {\rm{ t}} = \dfrac{{5 \times 100}}{{8 \times 6}}\\
 \Rightarrow {\rm{ t}} = \dfrac{{125}}{{12}}
\end{array}$
Hence, t = 10.41 years

Step 4
To convert the time period, t according to the options:
We know, 1 year = 12 months
          $\begin{array}{l}
0.41{\rm{ years}} = 0.41 \times 12{\rm{ months}}\\
{\rm{ = 4}}{\rm{.92 months}}\\
{\rm{ }} \simeq 5{\rm{ months}}
\end{array}$
Therefore, time period = 10 years and 5 months

Note:
When numbers of years are converted into days, it is always multiplied by 365, whether it is a leap year or an ordinary year.
Day on which the money is borrowed is not counted but the day on which the money is returned is counted.

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