Question

The C.I. on a sum of money for 2 years is Rs. 832 and the S.I. on the same sum for the same period is Rs. 800. The difference between the C.I. and S.I. for 3 years will be
A. Rs. 48
B. Rs. \[66.56\]
C. Rs. \[98.56\]
D. None of these

Answer 1

Hint: Here, we will first find the compound interest for 2nd year by subtracting the C.I. on a sum of money for 2 years by compound interest for 1st year and then use the formula of simple interest, \[{\text{S.I.}} = \dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{R}}\] is the interest rate per year and \[{\text{T}}\] is the time the money is invested in years to find the rate of interest. Then we will find the difference between the value of S.I. and C.I. for 3 years,

Complete step by step answer:

We are given that the C.I. on a sum of money for 2 years is Rs. 832 and the S.I. on the same sum for the same period is Rs. 800.

So we have that simple interest for 1st year is Rs 400 and the compound interest for 1st year with being Rs 400.

Now, finding the compound interest for 2nd year by subtracting the C.I. on a sum of money for 2 years by the compound interest for 1st year, we get

\[ \Rightarrow 832 - 400 = 432\]

We can now see that the compound interest for 2nd year is more than simple interest for 2nd year by subtracting the values, we get

\[ \Rightarrow 432 - 400 = {\text{Rs }}32\]

This implies that the simple interest Rs 32 is the interest obtained Rs 400 for 1 year.

We know that the formula of simple interest, \[{\text{S.I.}} = \dfrac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}}\], where \[{\text{P}}\] is principal starting amount of money, \[{\text{R}}\] is the interest rate per year and \[{\text{T}}\] is the time the money is invested in years.

First, we have to find the values of S.I.,\[{\text{T}}\] and \[{\text{P}}\] for the simple interest.
\[{\text{S.I.}} = 32\]
\[{\text{T}} = 1\]
\[{\text{P}} = 400\]

We will now substitute the above values to compute the rate using the above formula.

\[
  32 = \dfrac{{{\text{R}} \times 400 \times 1}}{{100}} \\
  32 = 4{\text{R}} \\
 \]

Dividing the above equation by 4 on both sides, we get

\[
   \Rightarrow \dfrac{{32}}{4} = \dfrac{{4{\text{R}}}}{4} \\
   \Rightarrow 8 = {\text{R}} \\
   \Rightarrow {\text{R}} = 8\% \\
 \]

Substituting the value of \[{\text{R}}\] in the above formula to find the simple interest obtained for Rs 832, we get

\[
   \Rightarrow {\text{S.I.}} = \dfrac{{832 \times 8 \times 1}}{{100}} \\
   \Rightarrow {\text{S.I.}} = \dfrac{{6656}}{{100}} \\
   \Rightarrow {\text{S.I.}} = {\text{Rs }}66.56 \\
 \]

Finding the difference between the value of S.I. and C.I. for 3 years, we get

\[
   \Rightarrow 0.1632 + 66.56 \\
   \Rightarrow {\text{Rs }}98.56 \\
 \]

Thus, the required value is Rs \[98.56\].

Hence, the option C is correct.

Note: In solving these types of questions, you should be familiar with the formulae of simple interest and compound interest. Students should note here that the sum of compound interest and simple interest is the principal amount. It is also important to understand in applying both the simple interest and compound interest formula accordingly. One should remember that simple interest is computed only on the principle, but the compound interest is calculated on both the accumulated interest and the principal.