A invests ₹8,000 and B invests ₹11,000 at the same rate of simple interest per annum. If, at the end of 3 year

Question

A invests ₹8,000 and B invests ₹11,000 at the same rate of simple interest per annum. If, at the end of 3 years, B gets ₹720 more interest than A, then find the rate of simple interest per annum.

Examoogle · Accepted Answer

The correct answer is Option D: 8%. Since the time and rate are the same, the difference in interest is simply the interest on the difference in principal amounts over 3 years.

Step-by-Step Solution & Concepts:
Shortcut Trick: Since the time and rate are the same, the difference in interest is simply the interest on the difference in principal amounts over 3 years.

Formula Used: $$I = \frac{P 	imes R 	imes T}{100}$$

Given: Principal for A ($P_A$) = ₹8,000, Principal for B ($P_B$) = ₹11,000, Time ($T$) = 3 years, Difference in interest ($I_B - I_A$) = ₹720

Steps: Identify Given Values: Principal invested by A is $P_A = ₹8,000$ and by B is $P_B = ₹11,000$. The time period is $T = 3$ years and the difference in interest received is $\Delta I = ₹720$.. Apply Simple Interest Formula on Difference: Since the rate $R$ and time $T$ are the same for both, the difference in interest is the interest on the difference in principal: $$\Delta I = \frac{\Delta P 	imes R 	imes T}{100}$$. Solve for Rate (R): Simplify the equation to find $R$: $720 = 90 	imes R$, which gives $R = \frac{720}{90} = 10\%$.

Answer: D is correct because the rate of simple interest calculated using the difference in principals is $10\%$.

Exam Tip: This shortcut of using the difference in principal can also be applied to compound interest problems for the first year or when comparing simple vs compound interest differences.

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