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 theother 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.

Correct option is A

Given:

Total amount invested = ₹2,00,000

One part yields 4% p.a. simple interest.

The other part yields 6% p.a. simple interest.

Total interest at the end of one year is equivalent to 4.7% p.a. on the whole amount.

Formula Used:

Simple interest formula:  $$\text{Interest} = \frac{P \times R \times T}{100}$$ 

Solution: ​

According to the condition:

​$$\frac{x \times 4 \times 1}{100} + \frac{(2,00,000 - x) \times 6 \times 1}{100} = \frac{2,00,000 \times 4.7 \times 1}{100} \\ \ \\ \frac{4x}{100} + \frac{6(2,00,000 - x)}{100} = \frac{940000}{100}$$​​

4x + 12,00,000 - 6x = 940000 

-2x + 12,00,000 = 9,400 

-2x = 940000 - 12,00,000

-2x = -2,60,000

x = 1,30,000

Thus,

Amount in Bank 1 (4% rate) = ₹1,30,000

Amount in Bank 2 (6% rate) = ₹70,000 

Alternate Solution: 

Alligation Method; 

Now , 7 + 13 = 2,00,000

20 unit = 2,00,000 

1 unit = 10,000 

So, 

Amount in Bank 1 (4% rate) = 13 $$\times$$ 10, 000 =  ₹1,30,000

Amount in Bank 2 (6% rate) = 7 $$\times$$ 10, 000 = ₹70,000