Question

A sum of Rs. 2500 deposited in a bank gives an interest of Rs. 100 in 6 months. What will be the interest on Rs. 3200 for 9 months at the same rate of interest?

Answer 1

Hint: First of all, find the interest for one year by multiplying the given interest for 6 months with 2. Now, apply the formula for simple interest $ S.I.=\dfrac{P\times R\times t}{100} $ and calculate the value of R. Here, P is the principal amount, R is the rate of interest and t is the time in years. Now, consider the second condition and calculate the value of S.I. for Rs. 3200 and 9 months.

Complete step by step answer:
Here, we have been provided that the bank provides an interest of Rs. 100 in 6 months, i.e half a year. So, we have
Interest provided by the bank in 1 year = $ 100\times 2=Rs.200 $
Now, we have to calculate the rate of interest first for Rs. 2500 that is deposited in the bank. This amount is considered as the principal amount. Now, applying the formula for simple interest, we have
 $ S.I.=\dfrac{P\times R\times t}{100} $
Here, S.I. = simple interest = Rs. 200
P = Principal amount = Rs. 2500
R = Rate
t = time in years = 1
Here we are taking t = 1 year because we have considered S.I. for one year and not half a year. So, we get,
 $ \begin{align}
  & \Rightarrow 200=\dfrac{2500\times R\times 1}{100} \\
 & \Rightarrow R=\dfrac{200\times 100}{2500} \\
 & \Rightarrow R=8 \\
\end{align} $
Therefore, the rate of interest is 8%.
Now, we have been asked to calculate the interest on Rs. 3200 for 9 months at the above obtained rate of interest. But first we need to convert the time in years.
 $ \because $ 12 months = 1 year
 $ \Rightarrow $ 9 months = $ \dfrac{1}{12}\times 9=\dfrac{3}{4} $ years
Therefore, applying the above simple interest formula, we get,
 $ S.I.=\dfrac{P\times R\times t}{100} $
Here, P = Rs. 3200
t = $ \dfrac{3}{4} $ years
R = 8%
Substituting these values, we get
 $ \begin{align}
  & \Rightarrow S.I.=\dfrac{3200\times 8\times \dfrac{3}{4}}{100} \\
 & \Rightarrow S.I.=Rs.192 \\
\end{align} $
Hence, the required interest for Rs. 3200 is Rs. 192.

Note:
One may note that we must convert the time given in months into time in years so that it can be substituted in the formula. You may note that while calculating the rate of interest (R) we have taken t = 1 years. This is because at the initial stage of the solution we had calculated the value of S.I. for 1 year. If we will take S.I = Rs. 100 then we must take t = $ \dfrac{1}{2} $ years.