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 months
B) 10 years and 5 months
C) 10 years and 4 months
D) 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.