Question

Divide 32,000 into two parts such that if one part is lent at 6% p.a. for 3 years and the other at 10% p.a. for 3 years, the total sum as interest is 6840..​

Answer 1

Answer:

32000 is divides as 23000 and 9000.

Step-by-step explanation:

Given that the total amount of money is 32000.

Let $x$ be one part of that and the other will be $32000-x$.

One part is lent at 6% annual interest for three years. That is

$I_1=\dfrac{x\times 3\times 6}{100}=\dfrac{18x}{100}$

Where $I_1$ is the interest and it is calculated using the formula

$I=\dfrac{p\times n\times r}{100}$

where $p$ is the principal amount, $n$ is the number of years, and $r$ is the annual rate of interest.

Similarly, the interest for the other part is,

$I_2=\dfrac{(32000-x)3\times 10}{100}=\dfrac{960000-30x}{100}$

Also, we know that the total interest is 6840. Thus,

$I_1+I_2=6840\\\\\implies \dfrac{18x}{100}+\dfrac{960000-30x}{100}= 6840\\\\\implies \dfrac{960000-12x}{100}=6840\\\\\implies960000-12x=684000\\\\\implies 12x=96000-684000=276000\\\\\implies x= \frac{276000}{12}=23000$

Since $x=23000$, the other part will be $32000-23000=9000$.