A total of ₹2,00,000 is divided into two parts for investing in different banks on simple interest. One yields 4% p.a. while the other yields 6% p.a. If the total interest at the end of one year is equivalent to 4.7% p.a. on the whole amount, the amount (in ₹) invested in each bank is ________, respectively.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1,30,000 and 70,000.
Total amount: ₹2,00,000
Interest rates: 4% p.a. and 6% p.a.
Combined interest rate: 4.7% p.a.
Let's use variables:
Let 'x' be the amount invested at 4% p.a.
Then, the amount invested at 6% p.a. is (2,00,000 - x).
Formulating the equation:
The total interest earned should be equal to the combined interest rate applied to the whole amount. We can express this as:
(x × 0.04) + ((2,00,000 - x) × 0.06) = 2,00,000 × 0.047
Solving the equation:
Expand the terms: 0.04x + 12,000 - 0.06x = 9,400
Combine like terms: -0.02x = -2,600
Solve for 'x': x = 1,30,000
Calculating the amounts:
Amount invested at 4% p.a.: ₹1,30,000
Amount invested at 6% p.a.: ₹2,00,000 - ₹1,30,000 = ₹70,000
Therefore, the amounts invested in each bank are ₹1,30,000 and ₹70,000, respectively.