Question

A certain sum of money Q was deposited for 5 years and 4 months at 4.5% simple interest and amounted to Rs 248. Then the value of Q is
A. Rs 200
B. Rs 210
C. Rs 220
D. Rs 240

Answer 1

Hint: Use the given values to calculate the simple interest with principal amount as variable and then equate the obtained result to the given interest to get the principal amount.

Complete step-by-step answer:
Given the problem, a certain sum of money Q was deposited for 5 years and 4 months at 4.5% simple interest.

The total interest received is Rs 258.

We know that simple interest is given by

Simple Interest = ${\displaystyle \frac{Q\times R\times T}{100}}\to$ (1)

Where $Q$ denotes the principal amount, $R$ denotes the rate of interest and $T$ denotes the time period.

It is given in the problem that the annual interest $R=4.5\mathrm{\%}$.

The time period for the deposit is given as 5 years and 4 months.

And the Simple Interest obtained is given as Rs 248.

We know that 12 months = 1 year

$\Rightarrow$1 month = ${\displaystyle \frac{1}{12}}$year

$\Rightarrow$4 months = ${\displaystyle \frac{4}{12}}={\displaystyle \frac{1}{3}}$year

Hence the total time period in years $T$$=5+{\displaystyle \frac{1}{3}}={\displaystyle \frac{16}{3}}$years .

Using the above in equation $(1)$, we get

$$\begin{gathered} 248={\displaystyle \frac{Q\times 4.5\times {\displaystyle \frac{16}{3}}}{100}} \\ \Rightarrow Q=248\times 100\times {\displaystyle \frac{3}{16}}\times {\displaystyle \frac{1}{4.5}}={\displaystyle \frac{24800}{124}}=200 \\ \Rightarrow Q=\text{Rs 200} \end{gathered}$$

Hence the principal sum of money deposited is equal to Rs 200.

Therefore, option (A). Rs 200 is the correct answer.

Note: Simple interest formula should be kept in mind while solving problems like above. The annual time period should be converted into the fractional years before using it into the formula. Also, the rate should be used as the numerical value given in percent as the percent part is already defined in the formula used above. Simple interest is calculated on the principal, or original, amount. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."