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)

A woman lent a total sum of Rs. 24000 from two moneylenders. For one loan, she paid interest at $7\frac{1}{2}\%$ p.a. and for the other $9\%$ p.a. How much money did she borrow at each rate ?

I. The sum of the interests after $1$ year was Rs. $2025$.

II. The interest on one sume was twice that the other.


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:

Suppose she borrowed Rs. $x$ at $7\frac{1}{2}\%$ p.a. and Rs. $(24000-x)$ at $9\%$ p.a.

I gives, total interest = Rs. $2025$.

$\therefore$ $\left(x\times 1\times\frac{15}{2}\times\frac{1}{100}\right)$ $+\left\{(24000-x)\times 1\times\frac{9}{100}\right\}$ $=2025$.

This gives $x$.

II gives interest on Rs. $(24000-x)$ $=2\times$ (interest on Rs. $x$).

$\Rightarrow (24000-x)\times\frac{9}{100}\times 1$ $=\left(2\times x\times\frac{15}{2}\times\frac{1}{100}\right)$

This gives $x$.

Thus I as well as II are suffficient to answer the question.

$\therefore$ Correct answer is (C).