Two equal sums of money are lent at simple interest: one sum is lent at 11% per annum for 5 years and the other equal sum is lent at 8% per annum for 6 years. If the difference between the simple interest earned on the two sums is Rs 1008, what is the value of each original sum lent based on the simple interest formula?

Introduction / Context:
This question checks your understanding of simple interest when two equal principals are invested at different rates and for different time periods. Instead of directly giving the principal, the problem gives the difference between the interests earned on the two sums. By forming and solving a simple algebraic equation using the standard simple interest formula, we can determine the value of each original sum of money.

Given Data / Assumptions:

Two equal sums are lent on simple interest.
First sum: rate = 11% per annum, time = 5 years.
Second sum: rate = 8% per annum, time = 6 years.
Difference between the simple interests on the two sums = Rs 1008.
Simple interest formula: SI = (P * R * T) / 100, where P is principal, R is rate, T is time in years.

Concept / Approach:
Let each original sum be P. We compute the simple interest on each sum using SI = (P * R * T) / 100. The problem states that the difference between these two interests is Rs 1008, which leads to a linear equation in P. Solving that equation gives the principal. Finally, we compare the numerical value of P with the options to identify the correct answer.

Step-by-Step Solution:
Step 1: Let each original sum = P rupees. Step 2: Simple interest on the first sum at 11% for 5 years: SI1 = (P * 11 * 5) / 100 = (55P) / 100. Step 3: Simple interest on the second sum at 8% for 6 years: SI2 = (P * 8 * 6) / 100 = (48P) / 100. Step 4: The difference between the two interests is given as SI1 - SI2 = 1008. Step 5: So, (55P / 100) - (48P / 100) = 1008. Step 6: This simplifies to (7P / 100) = 1008. Step 7: Therefore, P = 1008 * 100 / 7 = 100800 / 7 = 14400. Step 8: Hence, each original sum lent is Rs 14,400.

Verification / Alternative check:
Quickly verify by computing both interests with P = 14,400. First sum: SI1 = 14400 * 11 * 5 / 100 = 14400 * 55 / 100 = 7920. Second sum: SI2 = 14400 * 8 * 6 / 100 = 14400 * 48 / 100 = 6912. The difference = 7920 - 6912 = 1008, which matches the given difference. This confirms that P = 14,400 is correct.

Why Other Options Are Wrong:
For Rs 15,600, the interest difference is greater than 1008. For Rs 14,850, the difference is not exactly 1008. For Rs 15,220 and Rs 16,000, the computed differences also do not match 1008. Only Rs 14,400 satisfies the given condition precisely.

Common Pitfalls:
A frequent mistake is to add the rates or times incorrectly or to forget that the sums are equal and not separate unknowns. Another common error is to subtract interests in the wrong order, which can lead to a negative or incorrect value of P. Always carefully set up the equation SI1 - SI2 = given difference and then solve.

Final Answer:
The correct value of each original sum lent is Rs 14,400.