Discussion Forum



Each of the following question is followed by three statements, numbered I, II and III. Please read the question and all the three statements carefully and decide whether the question can be answered with any one or two statements or all the three statements. The answer number bearing the statements, which can be dispensed with, if any, while answering the question is your answer.

1)

What is the rate of interest per annum ?

I. The amount becomes Rs. $11,025$ with compound interest after $2$ years.

II. The same amount with simple interest becomes Rs. $11,000$ after $2$ years.

III. The amount invested is Rs. $10,000$.


A) I or II only

B) II or III only

C) I or III only

D) I or II or III only

E) All I, II and III are required

Answer:

Option D

Explanation:

I gives, Amount after $2$ years = Rs. $11025$, when compounded.

II gives, Amount after $2$ years at $S.I.$ = Rs. $11000$.

III gives, Principal = Rs. $10000$.

From II and III, we have :

Principal = Rs. $10000$, $S.I.$ = Rs. $(11000-10000)$ = Rs. $1000$ and Time = $2$ years.

Hence, Rate can be calculated.

$\therefore$ I is redundant.

From I and III, we get $11025$ $=10000\times \left(1+\frac{R}{100}\right)^{2}$. This gives $R$.

$\therefore$ II is redundant.

From I and II, we have

$P\left(1+\frac{R}{100}\right)^{2}$ $=11025$ ---(i)

and $P\left[1+\frac{R\times 2}{100}\right]$ $=11000$ ---(ii)

On dividing (i) by (ii), we get $\frac{\left(1+\frac{R}{100}\right)^{2}}{(50+R)}$ $=\frac{11025}{550000}$.

This gives $R$.

Thus, III is redundant.

Hence I or II or II is redundant.