Free
General Awareness Mock Test
10 Questions 10 Marks 10 Mins
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.