A sum becomes Rs. 2286 in 3 years and Rs. 2448 in 4 years at simple interest. What is the rate (in percentage) of interest per annum?a)10b)9c)8d)11Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given Data:
Amount after 3 years (A3) = Rs. 2286
Amount after 4 years (A4) = Rs. 2448

Formula for Simple Interest:
Simple Interest (SI) = PRT / 100

Calculating Simple Interest:
SI for 3 years = A3 - P
SI for 4 years = A4 - P

Calculation:
SI for 3 years = 2286 - P
SI for 4 years = 2448 - P

Calculating Rate of Interest:
SI for 3 years = P * R * 3 / 100
SI for 4 years = P * R * 4 / 100

Substitute the values:
(2286 - P) = 3PR / 100
(2448 - P) = 4PR / 100

Solving the Equations:
From the above equations, we get:
2286 - P = 300R
2448 - P = 400R

Subtract the Equations:
Subtracting the above equations, we get:
(2448 - P) - (2286 - P) = 400R - 300R
162 = 100R
R = 1.62%
Therefore, the rate of interest per annum is 9%.

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