Question

Ashok lent out Rs 7000 at 6% and 9500 at 5% interest. Find his total income from the interest in 3 years.
$
  A.{\text{ }}Rs.1966 \\
  B.{\text{ }}Rs.2133 \\
  C.{\text{ }}Rs.2685 \\
  D.{\text{ }}Rs.2948 \\
 $

Answer 1

Hint- For this case total, find out the respective simple interest for both the cases separately. The income will be interest earned by Ashok apart from his investment. Use the basic formula of simple interest.

Complete step-by-step solution -
Given that: Ashok lent out Rs 7000 at 6% and 9500 at 5% interest for 3 years.
As we know the basic formula of simple interest:
$SI = \dfrac{{P \times R \times T}}{{100}}$
Where SI is simple interest,
P is principal amount,
R is rate of interest and
T is the time period.
Let us find out the simple interest separately for both the cases
Case 1:
\[
  {P_1} = 7000 \\
  {R_1} = 6\% \\
  {T_1} = 3{\text{years}} \\
   \Rightarrow S{I_1} = \dfrac{{{P_1} \times {R_1} \times {T_1}}}{{100}} \\
   \Rightarrow S{I_1} = \dfrac{{7000 \times 6 \times 3}}{{100}} \\
   \Rightarrow S{I_1} = 1260 \\
 \]
Similarly for Case 2:
\[
  {P_2} = 9500 \\
  {R_2} = 5\% \\
  {T_2} = 3{\text{years}} \\
   \Rightarrow S{I_2} = \dfrac{{{P_2} \times {R_2} \times {T_2}}}{{100}} \\
   \Rightarrow S{I_2} = \dfrac{{9500 \times 5 \times 3}}{{100}} \\
   \Rightarrow S{I_2} = 1425 \\
 \]
So the net income is given by:
\[
  {\text{total income}} = S{I_1} + S{I_2} \\
   = Rs.1260 + Rs.1425 \\
   = Rs.2685 \\
 \]
Hence, total income of Ashok from interest in 3 years is Rs.2685.
So option C is the correct option.

Note- Remember the formula for simple interest as these types of questions requires direct use of formulas. Also when sum of money is divided in more than one part with different rates of interest or time period then always solve the problem separately. Simple interest is directly proportional to the rate of interest, principal amount and the time period.