In what time will the simple interest on a certain sum of money at 6 1 2 per annum be 3/8th of itself?

Let the sum of money be x

Amount = 3 × Rs x

= Rs 3x

Interest = Amount – Principal

= Rs 3x – Rs x

= Rs 2x

Rate =13 \frac{1}{3} \% \text { p.a. }

= 40 / 3 % p.a.

Time (T) = (I × 100) / (P × R)

= (2x × 100) / x × (40 / 3) years

On further calculation, we get,

= (2 × 100 × 3) / 40 years

= (100 × 3) / 20 years

We get,

= 5 × 3 years

= 15 years

If the simple interest on a certain sum of money after, 6 1/4 Years is 3/8 of the principal, then the rate of interest per annum is:

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Solution

The correct option is D 6%Let the sum of money be Rsx. Then, simple interest =38x Also, time =6 \frac{1}{4}years, i.e., \frac{25}{4}years\) ∴Rate(R)=100×IP×T=100×3x8x×254=100×32×25=6%

In what time will the interest on a certain sum of money at 6% be $\dfrac{5}{8}$of itself?A) 9 years and 4 monthsB) 10 years and 5 monthsC) 10 years and 4 monthsD) 9 years and 5 months

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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