Ajay took a loan with a principal amount of Rs.1400 with a simple interest for…

2023

Ajay took a loan with a principal amount of Rs.1400 with a simple interest for the same number of years as the rate. If his interest amount is Rs.686, calculate his rate of interest.

  1. A.

    6%

  2. B.

    7%

  3. C.

    5%

  4. D.

    4%

Show answer & explanation

Correct answer: B

Concept

Simple Interest is given by SI = (P × R × T) / 100, where P is the principal, R is the rate of interest per annum, and T is the time in years. When the time in years is stated to equal the rate (T = R), the formula reduces to a quadratic in R: SI = (P × R2) / 100.

Application

  1. Given: Principal P = Rs.1400, Simple Interest SI = Rs.686, and Time T equals Rate R (T = R).

  2. Substitute into SI = (P × R × T)/100, replacing T with R: 686 = (1400 × R × R)/100.

  3. Simplify the right side: 686 = 14 × R2.

  4. Divide both sides by 14: R2 = 49.

  5. Take the positive square root (rate cannot be negative): R = 7.

Cross-check

Substitute R = 7 and T = 7 back into the formula: SI = (1400 × 7 × 7)/100 = 68600/100 = 686, which exactly matches the given interest, confirming the rate.

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