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 total compound interest on a sum after $3$ years ?

I. The interest after one year was Rs. $100$ and the sum was Rs. $1000$.
II. The difference between simple and compound interest on a sum of Rs. $1000$ at the end of $2$ years was Rs. $10$.


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 C

Explanation:

I. gives : $P$ = Rs. $1000$ and $S.I$ for $1$ year = Rs. $100$.

$\therefore$ Rate $=\frac{100\times S.I.}{P\times T}$

$=\frac{100\times 100}{1000\times 1}$ $=10\%$ p.a.

Thus, $P$ = Rs. $1000$,$T=3$ years and $R=10%$ p.a.

$\therefore$ $C.I.$ may be obtained.

II. Sum = Rs. $1000$,$(C.I.)-(S.I.)$ for $2$ years = Rs. $10$.

Let the rate be $R\%$ p.a.

$1000\times\left[\left(1+\frac{R}{100}\right)^{2}-1\right]$ $-\left(\frac{1000\times R\times 2}{100}\right)$ $=10$.

From this, we can find $R$.

Thus $P$, $T$ and $R$ are given and therefore, $C.I$ may be calculated.

Thus, I alone as well as II alone is sufficient to get the answer.

$\therefore$ Correct answer is (C).