Question

The C.I. on a sum of money for $2$ years is $₹832$ and the S.I. on the same sum for the same period is $₹800$. The difference between the C.I and S.I. for $3$ years will be

Answer 1

Simple interest:

The simple interest for $2$ years $=800$.

Hence, S.I for $1$st year $=₹400$ and S.I for $2$nd year $=₹400$.

So, Compound interest for $1$st year will be Rs. 400.

So, C.I for $2$nd year $=832-400=432$

Hence, the difference between S.I and C.I for the $2$nd year $=432-400=₹32$.

Therefore, we can conclude that the interest obtained for $₹400$ for $1$year is $₹32$.

Therefore, the rate of interest $$\begin{gathered} =\frac{\left(100\times 32\right)}{\left(400\times 1\right)} \\ =8\% \end{gathered}$$

Now, we have to find the simple interest obtained for $₹832$$=832\times 8\times \frac{1}{100}=66.56$

The difference between C.I and S.I for $3$ years $$\begin{gathered} =32+66.56 \\ =₹98.56 \end{gathered}$$

Therefore, the total difference C.I and S.I for $3$ years $₹$$98.56$