Question

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

Answer 1

Hint: We will calculate the SI for ${1^{st}}$ year and it will be equal to CI for the ${1^{st}}$year and then we can calculate the CI and SI for the second year by reducing the ${1^{st}}$year’s CI and SI from the given of 2 years. Then, we will calculate the rate of interest for ${1^{st}}$ year by the formula: $R = \dfrac{{100 \times SI}}{{PT}}$ where SI is the simple interest, P is the principle cost and T is the time period. Then, the difference between CI and SI can be calculated by the SI obtained for Rs.832 at R interest rate for 1 year using the formula: $\dfrac{{PRT}}{{100}}$. We will add the difference between CI and SI for ${2^{nd}}$ and ${3^d}$ year to get the total difference for 3 years.

Complete step-by-step answer:
We are given that CI on a certain amount for 2 years is Rs.832 and SI for the same amount for 2 years is Rs.800.
We need to calculate the difference between CI and SI for 3 years.
First of all, we are given that SI for 2 years is Rs.800, therefore, SI for ${1^{st}}$ year will be Rs.400 (half of the SI). And, SI for ${2^{nd}}$ year will also be Rs.400.
Compound interest (CI) for the first year will be equal to the SI for first year i.e. CI for the ${1^{st}}$ year will be Rs.400.
Now, CI for the ${2^{nd}}$ year will be $Rs.832 - Rs.400 = Rs.432$, which is $Rs.32$ more than that of the ${1^{st}}$ year.
Therefore, the interest obtained for Rs.400 is Rs.32. We can calculate the rate of interest per annum as $R = \dfrac{{100 \times SI}}{{PT}}$, where SI is the simple interest, P is the principle cost and T is the time period.
\[ \Rightarrow R = \dfrac{{100 \times 32}}{{400 \times 1}} = 8\% \]
Now, the simple interest obtained for Rs.832 will be given by: SI = $\dfrac{{PRT}}{{100}}$
$ \Rightarrow SI = \dfrac{{832 \times 8 \times 1}}{{100}} = Rs.66.56$
Total difference between the compound and simple interest for 3 years will be the increase obtained over 3 years which is the sum of increase over $\left( {{2^{nd}} - {1^{st}}} \right)$ and $\left( {{3^{rd}} - {2^{nd}}} \right)$ years i.e.,
$ \Rightarrow $ Total difference = $Rs.32 + Rs.66.56 = Rs.98.56$
Therefore, the total difference between CI and SI for 3 years is Rs.98.56.
Hence, option (C) is correct.

Note: In this question, you may get confused at many places like when we calculate the rate of interest from the increase in CI over two years and then we used R to calculate SI. You may go wrong in the final step where we need to calculate the sum (or increase) in order to calculate the difference between CI and SI for 3 years.