Discussion Forum

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.

Answer:

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).