Ravi invests Rs P in Scheme A, which offers simple interest at 10% per annum for 2 years. He then invests the entire amount received from Scheme A (principal plus interest) in Scheme B, which offers simple interest at 12% per annum for 5 years. If the difference between the interest earned from Scheme A and Scheme B is Rs 1,300, what is the value of P?

Introduction / Context:
This question deals with successive investments in two simple interest schemes. Ravi first invests in a lower rate scheme, then reinvests the accumulated amount (principal plus interest) into a higher rate scheme for a longer period. The problem provides the difference between the interest earned in the second scheme and the first scheme and asks for the original principal. It combines basic simple interest calculations with algebraic reasoning about successive stages of investment.

Given Data / Assumptions:

Initial principal in Scheme A = Rs P
Scheme A rate = 10 percent per annum, time = 2 years
Amount from Scheme A is reinvested in Scheme B
Scheme B rate = 12 percent per annum, time = 5 years
Difference in interest (Scheme B minus Scheme A) = Rs 1,300
Both schemes use simple interest

Concept / Approach:
First, compute the simple interest earned in Scheme A in terms of P. Then determine the amount carried forward to Scheme B. Use that amount to compute the interest earned in Scheme B, again in terms of P. Finally, form an equation using the information that interest from Scheme B minus interest from Scheme A equals 1,300 rupees, and solve for P. The principal P will appear in both interest expressions but with different coefficients, which leads to a straightforward linear equation.

Step-by-Step Solution:
Step 1: Compute interest in Scheme A. Rate = 10 percent per annum, time = 2 years. I_A = P * 10 * 2 / 100 = P * 20 / 100 = 0.20 * P. Step 2: Compute amount after Scheme A. Amount after A = P + I_A = P + 0.20 * P = 1.20 * P. Step 3: Use this amount as principal in Scheme B. Principal in Scheme B = 1.20 * P. Rate in Scheme B = 12 percent per annum, time = 5 years. Step 4: Compute interest in Scheme B. I_B = (1.20 * P) * 12 * 5 / 100. I_B = 1.20 * P * 60 / 100 = 1.20 * P * 0.60 = 0.72 * P. Step 5: Difference between interests is given. I_B - I_A = 1,300 rupees. 0.72 * P - 0.20 * P = 1,300. Step 6: Simplify the left side: (0.72 - 0.20) * P = 0.52 * P. 0.52 * P = 1,300. Step 7: Solve for P: P = 1,300 / 0.52 = 2,500 rupees.

Verification / Alternative check:
Verify by substituting P = 2,500. Scheme A interest: I_A = 2,500 * 10 * 2 / 100 = 500 rupees. Amount after A = 2,500 + 500 = 3,000 rupees. Scheme B interest: I_B = 3,000 * 12 * 5 / 100 = 3,000 * 60 / 100 = 1,800 rupees. Difference I_B - I_A = 1,800 - 500 = 1,300 rupees, which matches the given condition. This confirms that the original principal is 2,500 rupees.

Why Other Options Are Wrong:
If P were 2,000, the difference in interests would be 0.52 * 2,000 = 1,040 rupees, not 1,300 rupees. For P = 3,000, the difference would be 1,560 rupees. For P = 3,500, the difference would be 1,820 rupees. None of these match the specified difference of 1,300 rupees. Only P = 2,500 rupees leads to the correct difference.

Common Pitfalls:
A common error is to treat Scheme B interest as if it were calculated on the original principal P rather than on the increased amount after Scheme A. Others might compute the difference between amounts instead of the difference between interests, which changes the equation. Another mistake is forgetting to divide by 100 when converting from percentage to decimal. Carefully tracking the flow of money from one scheme to the next and writing the algebraic expressions step by step is essential.

Final Answer:
The original principal invested by Ravi in Scheme A is Rs 2,500.