Two equal amounts were borrowed at 5% and 4% simple interest. The total interest after 4 yr amounted to Rs.405. What was the total amount borrowed?OptionsRs.1075Rs.1125Rs.1150Rs.1100

Let's solve this step by step:

1. Let's assume the equal amounts borrowed be 'P'. So, there are two amounts borrowed, each of 'P' value.

2. The total interest for 4 years for the first amount (at 5% simple interest) would be P54/100 = P/5.

3. Similarly, the total interest for 4 years for the second amount (at 4% simple interest) would be P44/100 = P/6.

4. Given that the total interest after 4 years is Rs.405, we can set up the equation as follows: P/5 + P/6 = 405.

5. To solve for 'P', we first find a common denominator for the fractions, which is 30. So, the equation becomes: 6P/30 + 5P/30 = 405.

6. Simplifying this gives: 11P/30 = 405.

7. Solving for 'P' gives: P = 405 * 30 / 11 = Rs.1100.

8. Since there were two amounts borrowed, the total amount borrowed would be 2P = 21100 = Rs.2200.

So, the total amount borrowed was Rs.2200. However, this option is not given in the question. There might be a mistake in the question or the options provided.

Let's denote the amount borrowed as P. Since the amounts borrowed are equal, we can say that the total amount borrowed is 2P.

The total interest for 4 years at 5% and 4% respectively would be calculated as follows:

Interest = Principal * Rate * Time

So, for the amount borrowed at 5%, the interest would be P * 5/100 * 4 = P/5 * 4 = 4P/5

Similarly, for the amount borrowed at 4%, the interest would be P * 4/100 * 4 = P/25 * 4 = 4P/25

The total interest is given as Rs. 405. So, we can set up the following equation:

4P/5 + 4P/25 = 405

To solve this equation, we first find a common denominator, which is 25. So, the equation becomes:

20P/25 + 4P/25 = 405

Adding the fractions on the left gives us:

24P/25 = 405

To solve for P, we multiply both sides of the equation by 25/24:

P = 405 * 25/24 = Rs. 421.875

Since the total amount borrowed is 2P, we multiply this by 2:

2P = 2 * 421.875 = Rs. 843.75

However, this is not one of the options given. It seems there might be a mistake in the problem or the options provided.