In what time will the interest on a certain sum of money at 6% per annum be 5 by 8 of itself?

Answer

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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 1Let the time period = t yearsLet the principle amount = P rupees Given:Rate % per annum on principal amount P = 6% Step 2Condition 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 3Here, 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 yearsStep 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

In 10 years and 5 months the interest on a certain sum of money at 6% will be $\dfrac{5}{8}$of itself. Thus, the correct option is (B).

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.

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

Let P = Rs.8

Interest = Rs.`8xx5/8` = Rs.5

R = 6%

T =`(100xx"I")/("P"xx"R")`

`=(100xx5)/(8xx6)`

`=500/48=125/12` years

`=10 5/12` years

= 10 years 5 months

`[∵ 5/12"year"=5/12xx12 "months"=5 "momths"]`

∴ Time = 10 years 5 months

Concept: To Find the Principle (P); the Rate Percent (R) and the Time