Question

Simple interest on a sum of money is $\frac{1}{3}$rd of the sum itself and number of years is thrice the rate percent. Find the rate of interest.

Answer 1

STEP 1 : Assuming all the given data in tho form of variables

Let the Principal (P) be $x$

Simple interest is $\frac{1}{3}rd$ of the Principal, (S.I.) $=\frac{1}{3}\times x=\frac{x}{3}$

Let the rate of interest (R) be $r\%$ per annum

Number of years is thrice the rate percent (T) $=3\times r=3r$

STEP 2 : Finding the rate of interest

Rate of interest (R) $=\frac{S.I.\times 100}{P\times T}=\frac{{\displaystyle \frac{x}{3}}\times 100}{x\times 3r}$

$r=\frac{100}{3\times 3r}=\frac{100}{9r}$

Transposing $r$ from L.H.S to R.H.S we get

$r\times r=\frac{100}{9}$

Taking square roots on both the sides we get

$\sqrt{r\times r}=\sqrt{\frac{100}{9}}$

$r=\frac{10}{3}=3\frac{1}{3}\%$

Hence, the rate of interest is $3\frac{1}{3}\%$ per annum.