Question : Mr Dutta desired to deposit his retirement benefit of 3 lakh partly to a post office and partly to a bank at 10% and 6% simple interests respectively. If his monthly interest was Rs. 2,000, then the difference between his deposits in the post office and the bank was:
Option 1: Rs. 50,000
Option 2: Rs. 40,000
Option 3: Nil
Option 4: Rs. 1,00,000
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Correct Answer: Nil
Solution :
Let the amount deposited in the bank and post office be Rs. $x$ and Rs. $(300000-x)$ respectively.
We know, interest = $\frac{PRT}{100}$, where $P$ is principal, and $R$ is the rate of interest per annum for $T$ years.
So, Interest gained from a 10% interest rate from Rs. $x$ in a year = Rs. $0.1x$
And Interest gained from a 6% interest rate from Rs. 3 Lacs in a year = Rs. $0.06(300000-x)$
Given, 1 month of interest income = 2000
So, 1 year interest income = 2000(12)= Rs. 24,000
Now, Total interest in a year = Interest from the bank + Interest from the post office
⇒ $24000 = 0.06(300000-x) + 0.1x$
⇒ $24000-18000 = 0.04x$
⇒ $x = 1,50,000$
⇒ $(300000 - x) = 1,50,000$
So, the Amount deposited = Rs. $1,50,000$ each
and difference = 0
Hence, the correct answer is 'Nil'.
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