Question

A person borrowed ${\text{Rs}}{\text{.80000}}$ from two known people. For one loan, he paid $18\% {\text{ p}}{\text{.a}}{\text{.}}$ and for second loan he paid $25\% {\text{ p}}{\text{.a}}{\text{.}}$. After a year, he paid ${\text{Rs}}{\text{.15800}}$ as simple interest. How much money did he borrow from each?

Answer 1

Hint: Let he borrowed ${\text{Rs}}{\text{.}}x$ from one person and ${\text{Rs}}{\text{.}}\left( {80000 - x} \right)$ from the other person. So, simple interest is given by either person$ = \dfrac{{P \times R \times T}}{{100}}$.
where $P$ is the principal, $R$ is the rate and $T$ is the time period. Now the rate is given $18\% {\text{ p}}{\text{.a}}{\text{.}}$ and $25\% {\text{ p}}{\text{.a}}{\text{.}}$

Complete step-by-step answer:
According to the question, a person borrowed ${\text{Rs}}{\text{.80000}}$ from two known people.
So, he borrowed ${\text{Rs}}{\text{.}}x$ from one person.
So total amount borrowed from second person$ = {\text{Rs}}{\text{.}}\left( {80000 - x} \right)$
He needs to pay the loan with rate $18\% {\text{ p}}{\text{.a}}{\text{.}}$ to one person and $25\% {\text{ p}}{\text{.a}}{\text{.}}$ to second person.
So, as we know the simple interest is given as $ = \dfrac{{P \times R \times T}}{{100}}$
Where, $P$ is the principal, $R$ is the rate and $T$ is the time period.
So, from the first person, he borrowed ${\text{Rs}}{\text{.}}x$.
So, principal$ = {\text{Rs}}{\text{.}}x$
And the rate is given $18\% {\text{ p}}{\text{.a}}{\text{.}}$ for $1$ year.
So,
interest$ = \dfrac{{x \times 18 \times 1}}{{100}} = \dfrac{{18x}}{{100}}$
now for second person,
He borrowed ${\text{Rs}}{\text{.}}\left( {80000 - x} \right)$ with interest $25\% {\text{ p}}{\text{.a}}{\text{.}}$
So,
Interest$ = \dfrac{{\left( {80000 - x} \right) \times 25 \times 1}}{{100}} = \left( {20000 - \dfrac{x}{4}} \right)$
And it is given that he has to pay ${\text{Rs}}{\text{.15800}}$ as total simple interest after a year.
Total interest
$
   = \dfrac{{18x}}{{100}} + \left( {20000 - \dfrac{x}{4}} \right) \\
  15800 = \dfrac{{9x}}{{50}} - \dfrac{x}{4} + 20000 \\
  \dfrac{x}{4} - \dfrac{{9x}}{{50}} = 20000 - 15800 \\
  \dfrac{{25x - 18x}}{{100}} = 4200 \\
  \dfrac{{7x}}{{100}} = 4200 \\
  x = \dfrac{{4200 \times 100}}{7} \\
  x = 60000 \\
 $
So, from the other person, he borrowed
$
  80000 - x \\
   = 80000 - 60000 \\
   = 20000 \\
 $
So, he borrowed ${\text{Rs}}{\text{.60000 and Rs}}{\text{.20000}}$ from those two known persons.

Note: Simple interest is based on the principal amount of a loan or deposit, and compound interest is based on the principal amount and the interest that accumulates on it in every period.
Simple interest is given by $ = \dfrac{{P \times R \times T}}{{100}}$
whereas compound interest is given by
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
where $A$ is the final amount.
$P$ is the initial principal amount.
$R$ is the interest rate.
$T$ is the number of time periods elapsed.