The interest earned on 8000 when invested in some scheme for 2 years at 7 % simple interest, per annum is half of the interest earned on another amount P invested for five years in the same scheme at the same rate of interest. Find the value of P.

Correct option is C

GIVEN:
• First principal = Rs. 8000
• Time = 2 years
• Rate = 7% per annum
• The interest earned on this is half the interest earned on another principal P invested for 5 years at the same rate.

FORMULA:
​$$SI = \frac{P \times R \times T}{100}$$​​

SOLUTION:
Step 1: Calculate interest on Rs. 8000 for 2 years
​$$SI_1 = \frac{8000 \times 7 \times 2}{100} = 1120$$​​

Step 2: Let the second amount be P, time = 5 years
Given:
1120 = (1/2) × SI₂
SI₂ = (P × 7 × 5) / 100
So:
1120 = (1/2) × (35P / 100)
Multiply both sides by 2:
2240 = (35P / 100)
Now solve for P:

​$$P = \frac{2240 \times 100}{35} \\\ \\P= \frac{224000}{35}\\\ \\P = 6400$$​​

Final Answer:
P = Rs. 6400
Correct Option: 3