Question

The simple interest on any amount is 2/9 of principal. If number of year is twice the rate of interest then for how many years that amount was given

Answer 1

If a number of years are twice the rate of interest then the amount was given for 6$\frac{2}{3}$ years.

Step-by-step explanation:

Let the principal be denoted as “P” and the no. of years be denoted as “T”.

It is given that,

The simple interest on any amount is 2/9th of the principal

i.e., S.I. = $\frac{2}{9}$ * P ….. (i)

Also, the no. of years is twice the rate of interest (R),  

i.e., T = 2 * R  

⇒ R = $\frac{T}{2}$ …. (ii)

The formula for the Simple Interest is given by,

S.I. = $\frac{PRT}{100}$

Substituting the values from (i) & (ii) in the formula, we get

$\frac{2}{9}$ * P = [P * $\frac{T}{2}$ *T] / 100

⇒ $\frac{2}{9}$ = [$\frac{T}{2}$ *T] / 100

⇒ T² = $\frac{2 * 100 * 2}{9}$

Taking square roots on both sides

⇒ T = $\frac{20}{3}$ years

⇒ T = 6$\frac{2}{3}$ years

Thus, the amount was given for 6$\frac{2}{3}$ years.

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