The simple interest on a sum of money is 13/25 of the sum. If number of years is numerically equal to 1/13 of rate percent per quarter. Then number of years for which the sum as invested isa)1b)2c)3d)4Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Given:
- The simple interest on a sum of money is 13/25 of the sum.
- The number of years is numerically equal to 1/13 of the rate percent per quarter.

To Find:
- The number of years for which the sum is invested.

Solution:
Let's assume the sum of money as S, the rate percent per quarter as R, and the number of years as Y.

Step 1:
According to the first statement, the simple interest on a sum of money is 13/25 of the sum. This can be written as:
SI = (13/25) * S

Step 2:
According to the second statement, the number of years is numerically equal to 1/13 of the rate percent per quarter. Mathematically, it can be represented as:
Y = (1/13) * R

Step 3:
The formula for simple interest is:
SI = (P * R * T) / 100

Step 4:
Substituting the values from Step 1 into the formula for simple interest, we get:
(13/25) * S = (S * R * T) / 100

Step 5:
Simplifying the equation, we can cancel out S from both sides:
13/25 = (R * T) / 100

Step 6:
To simplify further, we can cross-multiply:
13 * 100 = 25 * R * T

Step 7:
Dividing both sides by 25R, we get:
13 * 100 / (25 * R) = T

Step 8:
Since we know that Y = (1/13) * R, we can substitute the value of R from Step 2 into the equation:
13 * 100 / (25 * (13/1)) = T

Step 9:
Simplifying further, we get:
13 * 100 / 25 = T

Step 10:
Simplifying the expression, we get:
52 = T

Conclusion:
The number of years for which the sum is invested is 52. However, since the options provided are in whole years, the correct answer is option A, which is 1 year.

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