Question

What is the compound interest earned at the end of $3$ years?
I. Simple interest earned on that amount at the same rate and for the same period is $\text{Rs.}4500$.
II. The rate of interest is $10\%$ per annum
III. Compound interest for $3$ years is more than the simple interest for that period by $\text{Rs.}465$.

• A. I and II only
• B. II and III only
• C. I and III only
• D. Either II or III only
• E. Any two of the three

Answer 1

The correct option is D Either II or III only

I. gives, S.I. for $3$ years $=\text{Rs.}4500$. ---------(1)
II. gives, Rate$=10\%$ per annum -------------(2)
III. gives, $\text{C.I. - S.I.}=\text{Rs.}465$.
Clearly, using I and III we get, $\text{C.I.}=\text{Rs.}(465+4500)$.
Thus, II is redundant.

$\because$ Simple interest $=\frac{P\times R\times T}{100}$

$⟹P=\frac{\text{S.I.}\times 100}{R\times T}$ ----------(3)
$\therefore$ From (1), (2) and (3), we get $P=\left(\frac{100\times 4500}{10\times 3}\right)=\text{Rs}15,000$.
Now, Amount $=P{(1+\frac{R}{100})}^n$ where, $n$ is the number of years

$⟹\text{C.I.}=$ $\text{Amount}-P$
Thus, III is redundant.
$\therefore$ Either II or III is redundant.