Arithmetic aptitude :: Simple Interest :: Data Sufficiency 2

• Simple Interest - General Questions
• Simple Interest - Data Sufficiency 1
• Simple Interest - Data Sufficiency 2
• Simple Interest - Important Formulas and Facts

Principal :

The amount of money one borrows from a lender for a certain period of time is known as principal amount or the sum.

Interest :

Extra charge paid for the borrowed money is called Interest

Simple Interest (S.I.) :

Simple interest is a method to calculate the interest amount on a loan

Let Pricipal $=P$, Rate $=R\%$ per annum (p.a.) and Time $=N$ years. Then

(i) Simple interest (SI) $=\left(\frac{P\times N\times R}{100}\right)$

(ii) $P$ $=\left(\frac{100\times SI}{R\times N}\right)$ ; $R=\left(\frac{100\times SI}{P\times N}\right)$ and $N=\left(\frac{100\times SI}{P\times R}\right)$.

In how many years will a sum of money put at simple interest treble itself ?

I. The interest earned in $4$ years is half the sum.

II. The rate of interest is $12\frac{1}{2}\%$

III. The sum doubles itself in $8$ years at simple interest.

Answer:

Explanation:

Let sum Rs. $x$. Then, $SI$ = Rs. $(3x-x)$ = Rs. $2x$, $T$ = ?

I gives : When $T=4$, then $SI$ = Rs. $\frac{x}{2}$.

$\therefore R$ $=\frac{100\times SI}{P\times T}$

$=\left(100\times\frac{x}{2}\times\frac{1}{x}\times\frac{1}{4}\right)$

$=12\frac{1}{2}\%$ p.a.

Now, Sum = Rs. $x$, $SI$ = Rs. $2x$, $R=\frac{25}{2}\%$ p.a., $T$ = ?

$\therefore T$ $=\frac{100\times SI}{P\times R}$ $=\left(\frac{100\times 2x}{x\times 25}\times 2\right)$ $=16$ years.

Thus, I only gives the answer.

II gives, $R$ $=\frac{25}{2}\%$ p.a

$\therefore T$ $=\frac{100\times SI}{P\times R}$ $=\left(\frac{100\times 2x}{x\times 25}\times 2\right)$ $=16$ years.

Thus, II only also gives the answer.

III gives, $R=5\%$ p.a.

$\therefore T$ $=\frac{100\times SI}{P\times R}$ $=\left(\frac{100\times 2x}{x\times 5}\right)$ $=40$ years.

Thus, III only also gives the answer.

$\therefore$ Correct answer is (A).

• Simple Interest - General Questions
• Simple Interest - Data Sufficiency 1
• Simple Interest - Data Sufficiency 2