Question

Arun has a certain sum deposited in a bank at 5% per annum. The bank increases the rate of interest from 5% to 6%. After an increase in rates, Arun deposits Rs.2000 more in his account. The annual interest received by him now is Rs.220 more than before. Find his original deposit.
(A) Rs. 12,000
(B) Rs. 13,250
(C) Rs. 6,792
(D) Rs. 10,000

Answer 1

Hint: Assume that the original deposit that Arun deposits in the bank is Rs. x. Here, we have two cases. In the first case, it is given that the rate of interest equals 5%, principal money equal to Rs. x. We know that interest is paid by the bank at the end of every year. So, the time of interest is equal to 1 year. Now, use the formula, \[\text{Simple}\,\text{Interest=}\dfrac{\text{Principal }\!\!\times\!\!\text{ Rate }\!\!\times\!\!\text{ Time}}{\text{100}}\] and calculate the interest in the first case. In the \[{{2}^{nd}}\] case, it is given that the bank increases its rate of interest from 5% to 6%, and Arun deposits Rs.2000 more in his account. Now, the rate of interest equals 6%, principal money equal to Rs. \[\left( x+2000 \right)\] . We know that interest is paid by the bank at the end of every year. So, the time of interest is equal to 1 year. Now, use the formula, \[\text{Simple}\,\text{Interest=}\dfrac{\text{Principal }\!\!\times\!\!\text{ Rate }\!\!\times\!\!\text{ Time}}{\text{100}}\] and calculate the interest in the second case. It is given that Arun receives Rs. 220 more. It means that the interest received in the second case is Rs. 220 more than the interest received in the first case. Now, form an equation with the help of this information. Then, solve it further and get the value of x.

Complete step by step solution:
First of all, assume that the original deposit that Arun deposits in the bank is Rs. x.
Here, we have two cases.
In the \[{{1}^{st}}\] case, we have been given that the rate of the interest of the bank is 5%.
The rate of interest = 5% ……………………………..(1)
The principal money that Arun deposits = Rs. x ………………………………….(2)
We know that interest is paid by the bank at the end of every year.
The time of the interest = 1 year ……………………………………(3)
We know the formula, \[\text{Simple}\,\text{Interest=}\dfrac{\text{Principal }\!\!\times\!\!\text{ Rate }\!\!\times\!\!\text{ Time}}{\text{100}}\] …………………………………..(4)
Now, from equation (1), equation (2), equation (3), and equation (4), we get
The interest that is paid by the bank = \[\dfrac{x\times 5\times 1}{100}=\dfrac{5x}{100}\] …………………………………..(5)
In the \[{{2}^{nd}}\] case, we have been given that the bank increases its rate of interest from 5% to 6%, and Arun deposits Rs.2000 more in his account.
The rate of interest = 6% ……………………………..(6)
The principal money that Arun deposits = Rs. \[\left( x+2000 \right)\] ………………………………….(7)
Since the bank pays interest at the end of every year so, the time for the interest is 1 year.
The time for the interest = 1 year ……………………………………(8)
Now, from equation (4), equation (6), equation (7), and equation (8), we get
The interest that is paid by the bank = \[\dfrac{\left( x+2000 \right)\times 6\times 1}{100}=\dfrac{6\left( x+2000 \right)}{100}\] …………………………………..(9)
From equation (5) and equation (9), we have interest received in the first second case and the second case.
We have been given that Arun receives Rs. 220 more. It means that the interest received in the second case is Rs. 220 more than the interest received in the first case. So,
\[\begin{align}
  & \Rightarrow Rs.\dfrac{5x}{100}+Rs.220=Rs.\dfrac{6\left( x+2000 \right)}{100} \\
 & \Rightarrow \dfrac{5x}{100}+220=\dfrac{6\left( x+2000 \right)}{100} \\
 & \Rightarrow 5x+22000=6x+12000 \\
 & \Rightarrow 22000-12000=6x-5x \\
 & \Rightarrow 10000=x \\
\end{align}\]
Therefore, the original deposit in the bank is Rs. 10,000.
Hence, the correct option is (D).

Note: In this question, one might assume that Arun deposits Rs. x for y years. Since the bank pays interest at the end of every year so, the time for the interest is 1 year. Therefore, we don’t need to assume the time for the interest. We can take the time for the interest equal to 1 year.