A person borrows two equal sums of money at the time at 5% and 3.75% simple interest respectively & finds that if he repays the former sum a year before the latter the amount paid in each case is the same that is Rs.736. Find the total sum borrowed.

Let's assume that the total sum borrowed is "P" rupees.

According to the given information, the first sum is borrowed at 5% simple interest and the second sum is borrowed at 3.75% simple interest.

The interest for the first sum borrowed at 5% is calculated as (P * 5% = 0.05P) for each year.

Since the borrower repaid the first sum a year before the second sum, the interest for the second sum is calculated for (1 - 1 = 0) years, which means no interest is added to the second sum.

The total amount repaid for both sums is Rs. 736. So, the sum of the borrowed amount and interest for the first sum should be equal to Rs. 736.

Therefore, we can set up the equation:
P + 0.05P = 736

Simplifying the equation:
1.05P = 736

Divide both sides by 1.05:
P = 736 / 1.05

Calculating the value of P:
P ≈ 700

Hence, the total sum borrowed is approximately Rs. 700.

To find the total sum borrowed, we can follow these steps:

Step 1: Let's assume the sum borrowed is 'x' rupees.

Step 2: Calculate the interest for the first sum at 5% for one year. We use the formula: Simple Interest = (Principal * Rate * Time) / 100.

Interest for the first sum = (x * 5 * 1) / 100 = 5x/100 = x/20.

Step 3: Calculate the interest for the second sum at 3.75% for one year.

Interest for the second sum = (x * 3.75 * 1) / 100 = 3.75x/100 = 3x/80.

Step 4: Since he repays the first sum a year before the second sum, we deduct the interest from the principal amount he actually received.

Amount paid for the first sum = x - (x/20) = 19x/20.
Amount paid for the second sum = x - (3x/80) = 77x/80.

Step 5: According to the given information, both amounts paid are the same, i.e., 19x/20 = 77x/80.

Cross-multiplying, we get: 19x * 80 = 77x * 20.
Simplifying, we have: 1520x = 1540x.
By canceling out 'x' from both sides, we find: 1520 = 1540.

Step 6: This equation is not true, which means our assumption of 'x' is incorrect. Therefore, there is no solution to this problem, and we cannot find the total sum borrowed.

In this case, it appears there might be an error in the given question or information provided. I suggest double-checking the question or seeking clarification if possible.

Solution

.05(n-1)x = 736

.0375nx = 736

Now just solve for x, then double it.