Question

At what rate will a certain amount of money be doubled at a simple interest rate of 12% per annum?​

Answer 1

Answer:

Since it is mentioned that the interest is simple, we can simply divide 100 by 12 to get the time period…that would be 8 years and 4 months.

100 / 12 = 8 and 1/3 = 8 years and 4 months.

There is another approach for the same problem.

Since we are given the interest rate as 12% Simple Interest - it means the rate of interest is 1 percent per month…1 rupee per month on 100 rupees…so, it would take 100 months to get 100 rupees interest and thus double the original amount…

!00 months is 8 years and 4 months.

Answer 2

Correct Question:

• In what time period will a certain amount of money be doubled at a simple interest rate of 12% per annum?

Answer:

$\sf{\circ\;Time\;period \;is\;8\dfrac{1}{3}\;years.}$

Step-by-step explanation:

Let us assume:

• Sum of money be x.

Then,

• Amount will be 2x.

As we know that,

• Simple Interest = Amount - Principal

Substituting the values,

Simple Interest = 2x - x

= x

Hence, Simple Interest is x.

Now, let us assume:

• Time period be t.

And, its given that:

• Simple Interest rate = 12%

Then, according to the question:

$\rm{\longmapsto x=\dfrac{x\times12\times t}{100}}$

Transposing 100 from RHS to LHS and changing its sign,

$\rm{\longmapsto x\times100=x\times12\times t}$

Cutting like terms on both sides,

$\rm{\longmapsto \not{x}\times100=\not{x}\times12\times t}$

$\rm{\longmapsto 100=12\times t}$

Transposing 12 from RHS to LHS and changing its sign,

$\rm{\longmapsto \dfrac{100}{12}= t}$

Reducing the numbers,

$\rm{\longmapsto \dfrac{100\div4}{12\div4}= t}$

$\rm{\longmapsto \dfrac{25}{3}= t}$

Converting the improper fraction into mixed fraction,

$\rm{\longmapsto 8\dfrac{1}{3}= t}$

$\rm{\longmapsto t=\dfrac{25}{3}}$

Hence,

$\sf{\circ\;Time\;period \;is\;\bf{8\dfrac{1}{3}\;years}.}$