At what rate percent simple interest will a sum of money amount to 5/3 of itself in 6 years 8 months?

Answer

Hint:- In 8 years money from Interest will be come equal to the principal
amount invested. So, money had been doubled in 8 years.

Let the initial amount of money invested will be Rs. x.
Then after 8 years money had become 2x.
Out of Rs. 2x, money from interest will be 2x – initial amount invested = 2x – x = x.
Let the rate of interest be r.

So, now we will use a simple interest formula.
According to Simple Interest (S.I) formula.
\[ \Rightarrow S.I. = \dfrac{{PRT}}{{100}}\]. Where P is principal amount, R is rate of interest and T will be time period.

So, putting the values in the above formula. We will get,
\[ \Rightarrow x = \dfrac{{xr(8)}}{{100}}\]
On solving the above equation. We will get,
\[ \Rightarrow {\text{ }}r{\text{ }} = {\text{ }}\dfrac{{100}}{8}{\text{ }} = {\text{ }}12.5\]

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

Note:- Whenever we came up with this type of problem where we are asked to
find rate of interest then first, we will find the interest on principal amount by
subtracting principal amount from the money after 8 years and then we will
assume rate of interest to be r and then apply, Simple Interest formula and
find the required value of rate of interest.

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CT 1: Growth and Development - 1

10 Questions 10 Marks 10 Mins

Given:

Time = 3 years

Amount ∶ Principal = 7 ∶ 4 

Formula Used:

Interest = Amount – Principal

Simple interest = Principal × Interest Rate × Time /100

Calculation:

Amount/Principal = 7/4

So, Principal = 4x

And, Amount = 7x

Interest = Amount – Principal

⇒ 3x = 7x - 4x

Simple interest = Principal × Interest Rate × Time /100

⇒ 3x = 4x × R × 3/100

⇒ R = 25% p.a.

∴ The rate of interest is 25% p.a.

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CT 1: Current Affairs (Government Policies and Schemes)

10 Questions 10 Marks 10 Mins

Given:

Amount ∶ Principal = 6 ∶ 5

Time = 8 years

Formula Used: 

Simple interest = Amount -  Principal

Simple interest = (Principal × Time × Rate of interest)/100

Calculation:

Let assume that principal = 5x

Amount = 6x

⇒ Simple interest = 6x - 5x = x

⇒ x = (5x × 8 × Rate of interest)/100

∴ Rate of interest = 2.5% p.a. 

The correct option is 3 i.e. 2.5% p.a.

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A sum of money becomes 8 / 5 of itself in 5 years at a certain rate of simple interest .find the rate of interest.

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Solution

Given: Time, T=5 yearsLet the principal be PRate of interest =R Amount, A=8P5Simple Interest, S.I= Amount − Principal =8P5−P=3P5 ∴S.I=3P5 Again, S.I=P×R×T100⇒3P5=P×R×5100⇒35=5R100⇒35=R20⇒R=3×205 (adsbygoogle = window.adsbygoogle || []).push({}); ⇒R=3×4∴R=12. The required rate of interest is 12%.

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