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?

To solve this problem, we need to use the formula for simple interest which is I = PRT/100, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest, and T is the time in years.

Given that the total interest after 4 years is Rs.405 and the rates of interest are 5% and 4%, we can set up two equations to represent the two amounts borrowed.

Let's denote the equal amounts borrowed as P. The total interest is the sum of the interests from the two amounts borrowed.

So, we have:

I1 = PRT/100 = P54/100 = P/5 (This is the interest from the first amount borrowed)

I2 = PRT/100 = P44/100 = P/6.25 (This is the interest from the second amount borrowed)

The total interest is I1 + I2 = P/5 + P/6.25 = Rs.405

To solve for P, we add the fractions on the left side of the equation:

P/5 + P/6.25 = 405

Multiply through by 25 to clear the denominators:

5P + 4P = 405*25

9P = 10125

Divide by 9 to solve for P:

P = 10125 / 9 = Rs.1125

So, each amount borrowed was Rs.1125. Since there were two equal amounts borrowed, the total amount borrowed was 2P = 21125 = Rs.2250.

Let's solve this step by step:

Step 1: Let's assume the equal amounts borrowed be 'P'. So, the total amount borrowed is '2P'.

Step 2: According to the problem, the total interest for 4 years is Rs.405. This interest is the sum of the interests from both the amounts borrowed.

Step 3: We know that the formula for simple interest is I = PRT/100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years.

Step 4: So, the interest from the first amount is (P54)/100 and from the second amount is (P44)/100.

Step 5: Adding these two interests gives us the total interest, which is Rs.405. So, we have the equation (P54)/100 + (P44)/100 = 405.

Step 6: Simplifying this equation gives us (20P + 16P)/100 = 405, which further simplifies to 36P/100 = 405.

Step 7: Solving for P, we get P = (405 * 100) / 36 = Rs.1125.

Step 8: So, the total amount borrowed is 2P = 2*1125 = Rs.2250.