Shortcut Trick
Effective interest in 1st case = 7.5% × (10/3) = 25% → Amount = 125% of Principal.
Effective interest in 2nd case = 8% × (15/4) = 30% → Amount = 130% of Principal.
Since 125% of Principal = ₹4900
130% of Principal = (4900 ÷ 125) × 130 = 39.2 × 130 = ₹5096.
∴ The correct answer is ₹5096.
Alternate Method
Given:
Amount in 1st case (A1) = ₹4900
Rate (R1) = 7.5% p.a., Time (T1) = 3 years 4 months = 3 + 1/3 = 10/3 years
Rate (R2) = 8% p.a., Time (T2) = 3 + 3/4 = 15/4 years
Formula Used:
Simple Interest (SI) = (P × R × T) ÷ 100
Amount (A) = P + SI = P × (1 + RT/100)
Sum (P)
A₁ = 4900
7.5% for 10/3 yr
SI = +25%
A₂ = 5096
8% for 15/4 yr
SI = +30%
Calculations:
⇒ In the 1st case, SI1% = 7.5 × (10/3) = 25%
⇒ Amount (A1) = 100% + 25% = 125% of P
⇒ 125% of P = ₹4900
⇒ P = (4900 × 100) ÷ 125 = ₹3920
⇒ In the 2nd case, SI2% = 8 × (15/4) = 30%
⇒ Amount (A2) = 100% + 30% = 130% of P
⇒ A2 = 130% of 3920 = (130 ÷ 100) × 3920
⇒ A2 = 1.3 × 3920 = ₹5096
∴ The correct answer is ₹5096.
Additional Information
Effective Interest Rate in SI
In Simple Interest, the effective interest percentage for a given period is simply the product of the rate and time (R × T)%. This allows for direct calculation without finding the principal every time.
Amount Formula for Simple Interest
Amount (A) = P + SI = P(1 + RT/100). The principal remains constant throughout the entire period, unlike compound interest where interest is added to the principal.
Simple vs Compound Interest
For the first year, both simple and compound interests are identical (if compounded annually). From the second year onwards, CI will be greater than SI because interest is earned on accumulated interest.