Question

Karim deposited a sum of Rs. 9000 in a bank. After 2 years, he withdrew Rs. 4000 and at the end of 5 years, he received Rs. 8300. Find the interest on the sum he received.

Answer 1

Hint: First, we will 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 and then use the given conditions to find the required value.

Complete step-by-step answer:
Let us assume that R represents the rate of interest per annum.
We are given that Karim deposited a sum of Rs. 9000 in a bank. SO, we have principal P is Rs 9000.
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 value of T and P for the above formula of simple interest.
\[{\text{P}} = 9000\]
\[{\text{T}} = 2\]
We will now substitute the above value, P and T to compute the simple interest using the above formula.
\[
   \Rightarrow {\text{S.I.}} = \dfrac{{9000 \times {\text{R}} \times 2}}{{100}} \\
   \Rightarrow {\text{S.I.}} = 180{\text{R}} \\
 \]
So, the total amount after 2 years, \[{\text{A}} = 9000 + 180{\text{R}}\].
Now, when Suhani withdraw 4000 rupees from her account, we get
\[
   \Rightarrow 9000 + 180{\text{R}} - {\text{4000}} \\
   \Rightarrow 5000 + 180{\text{R}} \\
 \]
Now for the second case, we know that the simple interest is applied only on the initial principal amount not the whole amount, otherwise it will be compound interest.
So, our principal is 5000 rupees and the time taken is after 3 years.
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 value of P and T for the above formula of simple interest.
\[{\text{P}} = 5000\]
\[{\text{T}} = 3\]
We will now substitute the above value, P and T to compute the simple interest using the above formula.
\[
   \Rightarrow {\text{S.I.}} = \dfrac{{5000 \times {\text{R}} \times 3}}{{100}} \\
   \Rightarrow {\text{S.I.}} = 150{\text{R}} \\
 \]
Since we know she received in last 8300, so we have
\[
   \Rightarrow 180{\text{R}} + 150{\text{R}} + 5000 = 8300 \\
   \Rightarrow 330{\text{R}} + 5000 = 8300 \\
 \]
Subtracting the above equation by 5000 on both sides, we get
\[
   \Rightarrow 5000 + 330{\text{R}} - 5000 = 8300 - 5000 \\
   \Rightarrow 330{\text{R}} = 3300 \\
 \]
Dividing the above equation by 330 on both sides, we get
\[
   \Rightarrow \dfrac{{330{\text{R}}}}{{330}} = \dfrac{{3300}}{{330}} \\
   \Rightarrow {\text{R}} = 10{\text{% }} \\
 \]
Hence, the interest rate is \[10\% \].

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 or else the answer will be wrong.