Shortcut Trick
Let the Principal amount be 100%.
First Simple Interest (SI1) = 5% × 5 years = 25% of Principal
Second Simple Interest (SI2) = 4% × 4 years = 16% of Principal
Difference in interest = 25% − 16% = 9% of Principal
Given that this difference is Rs. 900:
⇒ 9% of Principal = Rs. 900
⇒ 100% of Principal = (900 ÷ 9) × 100 = Rs. 10,000
∴ The correct answer is Rs. 10,000.
Alternate Method
Given:
• Rate of interest for first case (R1) = 5% per annum
• Time period for first case (T1) = 5 years
• Rate of interest for second case (R2) = 4% per annum
• Time period for second case (T2) = 4 years
• Difference between the two simple interests = Rs. 900
Formula Used:
Simple Interest (SI) = (P × R × T) ÷ 100
Where P = Principal amount, R = Rate of interest per annum, and T = Time period in years.
Calculations:
Let the Principal amount be P.
For the first case:
⇒ SI1 = (P × 5 × 5) ÷ 100
⇒ SI1 = 25P ÷ 100
For the second case:
⇒ SI2 = (P × 4 × 4) ÷ 100
⇒ SI2 = 16P ÷ 100
According to the question, the difference between the two interests is Rs. 900:
⇒ SI1 − SI2 = 900
⇒ (25P ÷ 100) − (16P ÷ 100) = 900
⇒ (25P − 16P) ÷ 100 = 900
⇒ 9P ÷ 100 = 900
⇒ 9P = 900 × 100
⇒ 9P = 90000
⇒ P = 90000 ÷ 9
⇒ P = 10000
Thus, the principal amount is Rs. 10,000.
Explanation of other options:
• Option (1) Rs. 9,000: If P = Rs. 9,000, then SI1 = (9000 × 25) ÷ 100 = Rs. 2,250 and SI2 = (9000 × 16) ÷ 100 = Rs. 1,440. The difference is Rs. 810, which is incorrect.
• Option (2) Rs. 10,500: If P = Rs. 10,500, then SI1 = (10500 × 25) ÷ 100 = Rs. 2,625 and SI2 = (10500 × 16) ÷ 100 = Rs. 1,680. The difference is Rs. 945, which is incorrect.
• Option (4) Rs. 12,000: If P = Rs. 12,000, then SI1 = (12000 × 25) ÷ 100 = Rs. 3,000 and SI2 = (12000 × 16) ÷ 100 = Rs. 1,920. The difference is Rs. 1,080, which is incorrect.
∴ The correct answer is Rs. 10,000.
Additional Information
Simple Interest (SI)
SI = (P × R × T) ÷ 100, where P is Principal, R is Rate of Interest per annum, and T is Time in years.
Total Amount (A)
A = Principal (P) + Simple Interest (SI) = P × (1 + (R × T) ÷ 100).
Difference between SI and CI for 2 Years
Difference (D) = P × (R ÷ 100)2.