A sum of money at simple interest doubles itself in 8 years in how much time will it be three times

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.

A sum of money at simple interest doubles in 8 years. In how many years it will become 8 times at the same rate of interest.

1. 16 years
2. 32 years
3. 56 years
4. 64 years

Answer (Detailed Solution Below)

Option 3 : 56 years

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Navik Section I: Official Model paper

60 Questions 60 Marks 45 Mins

If a sum of money becomes ‘n1’ times in 'T1’ years and 'n2’ times in 'T2’ years at simple interest, then

(n1 - 1)/(n2 - 1) = (T1)/(T2) 

(2 - 1)/(8 -1) = (8)/(T2)

⇒ 1/7 = (8)/(T2)

⇒ T2 = 56 years

∴ The time taken to 8 times the amount is 56 years.

Given:

Amount = 2P

Time = 8 years

Formula Used:

S.I = (PRT/100) + P

Amount = S.I + P

Where,

S.I = Simple interest

P = Principal

R = Rate of interest 

T = Time duration

Calculation:

Let the principal be P

⇒ S.I = 2P - P

⇒ S.I = P

According to the question, we have 

P = (P × R × 8)/100 

⇒ R = 100/8

⇒ R = 12.5%

Now, the principal increase 8 times itself

S.I = 8P - P

⇒ S.I = 7P

7P = (P × 12.5 × T)/100 

⇒ 7 = T/8

⇒ T = 8 × 7

⇒ T = 56 years

∴ The time taken to 8 times the amount is 56 years.

Interest = 2P - P

⇒ P = 100% of principle

Time = 8 years

Rate = Interest/Time 

⇒ 100/8 = 12.5%

New interest = 8P - P

⇒ 7P = 700% of principle

Time = Interest/Rate

⇒ 700/12.5 

⇒ 56 Years

∴ The time taken to 8 times the amount is 56 years.

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hello the question a sum of money invested at the certain rate of interest Doubles itself in the initial amount becomes available in 8 years in how much time it will trouble itself at the same rate of interest in this question we have to calculate the time required for the the amount becomes three times of itself so let's solve the problem let the initial amount let the principal amount initial amount means principal amount is X rupees rupees ex after 8 years after 8 year

it becomes double itself means to Times of text initially it is ex after 8 years it becomes too x x so put the least value in the formula of simple interest we get the value of rate of interest the formula of simple interest S is equals to x x divided by 100 if the initial amount is ex after a tear it becomes too X means Din dresses intereses X rupees is added so put the value of x means X the initial amount interest is so the total amount becomes two times of its so put the value of simple interest

x is equal to principal amount is also a rate of interest is unknown are as it is time period is 8 years divided by 100 yaar hundred is divided after shifting it becomes multiply so x x 100 / 8 into X is equals to are so the rate of interest near XX Gate cancel 100/8 so Ande / this calculation 8182 is remaining eight to the 16 for his remaining for means give decimal after that it becomes 4240 upon 8 means 5 the rate of interest is 12% per annum

using same formula we can calculate the time so formula is yes I is equals to Pintu hour into it divided by 100 show in second condition the initial amount is it but after time period t it becomes Triple IT cell means three times of its the subtraction of both is means the indices 2x is added so that the value of simple interest to Times of access principal amount is eggs rate of interest is 12.5 into time period t / so year 2 x 100 / 12.5 x of x is equals to 3 x x get cancer

12.5 so year 112.5 is a 2 x 8 the answer is 16 years so answer of your question is after 16 year the initial amount becomes three times of itself thank you

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