Discussion Forum



Each of the questions given below consists of two statements numbered I and II given below it. Please read the questions carefully and decide whether the data provided in the statement(s) is / are sufficient to answer the given question.

1)

What was the rate of interest on a sum of money ?

I. The sum fetched a total of Rs. $2522$ as compound interest at the end of $3$ years.

II. The difference between the simple interest and the compound interest at the end of $2$ years at the same rate was Rs. $40$


A) I alone sufficient while II alone not sufficient to answer

B) II alone sufficient while I alone not sufficient to answer

C) Either I or II alone sufficient to answer

D) Both I and II are not sufficient to answer

E) Both I and II are necessary to answer

Answer:

Option E

Explanation:

I gives : $C.I$ for $3$ years = Rs. $2522$.

II gives : $(C.I)-(S.I)$ for $2$ years at same rate is Rs. $40$.

$\left[\left(1+\frac{R}{100}\right)^{3}-1\right]$ $=2522$ ---(i)

$\left[\left(1+\frac{R}{100}\right)^{2}-1\right]$ $-\frac{P\times R\times 2}{100}$ $=40$ ---(ii)

On dividing (i) by (ii) we get :

$\frac{\left(1+\frac{R}{100}\right)^{3}-1}{\left(1+\frac{R}{100}\right)^{2}-1-\frac{R}{50}}$ $=\frac{2522}{40}$

$\Rightarrow \frac{\frac{R^{3}}{1000000}+\frac{3R}{100}+\frac{3R^{2}}{10000}}{\frac{R{2}}{10000}}$ $=\frac{1261}{20}$

$\Rightarrow \frac{R}{100}$ $+\frac{300}{R}$ $=\frac{1201}{20}$ $\Rightarrow R^{2}$ $-6005R$ $+30000$ $=0$

$\Rightarrow R^{2}-6000R$ $-5R+30000$ $=0$

$\Rightarrow R(R-6000)$ $-5(R-6000)$ $=0$

$\Rightarrow (R-5)(R-6000)$ $=0$

$\Rightarrow R=5$

$\therefore$ Both I and II are needed to get $R$.

$\therefore$ Correct answer is (E).