A sum of money becomes 7/6 of itself in 3 years at a certain rate of simple interest. What is the rate of interest per annum corresponding to this growth factor?

Introduction / Context:
This question expresses the final amount as a fraction of the original principal under simple interest. When the amount becomes 7/6 of the principal in a certain time, you can use the relationship between amount, principal, and simple interest to find the annual rate. Such problems encourage you to work with fractions and ratios instead of only absolute rupee values.

Given Data / Assumptions:

Let principal P be the original sum of money.
Time T = 3 years.
Amount A after 3 years = (7/6) * P.
Simple interest SI = A - P.
Rate of interest per annum = r% (unknown).
Simple interest formula: SI = (P * r * T) / 100.

Concept / Approach:
Since the amount is 7/6 of the principal, we can determine the fraction of the principal that constitutes the interest. That fraction over 3 years directly gives us the total interest in terms of P. Equating that to the simple interest formula yields an equation involving r that we then solve. Expressing r as a fraction ensures we match the options given in fractional percent form.

Step-by-Step Solution:
Step 1: Amount A after 3 years is given as (7/6)P. Step 2: Simple interest SI = A - P = (7/6)P - P. Step 3: Simplify SI = (7/6)P - (6/6)P = (1/6)P. Step 4: Thus, over 3 years the interest is (1/6) of the principal. Step 5: Using SI formula: SI = (P * r * T) / 100 = (P * r * 3) / 100. Step 6: Equate the two expressions for SI: (P * r * 3) / 100 = (1/6)P. Step 7: Cancel P from both sides (P is nonzero): (r * 3) / 100 = 1 / 6. Step 8: Multiply both sides by 100: 3r = 100 / 6. Step 9: Simplify 100 / 6 = 50 / 3, so 3r = 50 / 3. Step 10: Divide both sides by 3: r = (50 / 3) / 3 = 50 / 9. Step 11: Therefore, the rate of interest per annum is 50/9%.

Verification / Alternative check:
To verify, compute the amount using r = 50/9%. Simple interest for 3 years is SI = (P * (50/9) * 3) / 100 = (P * 50 * 3) / (9 * 100) = (150P) / 900 = (1/6)P. Amount A = P + SI = P + (1/6)P = (7/6)P, which matches the given growth factor, confirming the rate is correct.

Why Other Options Are Wrong:
Rates like 45/7%, 51/7%, 47/9%, or 40/9% do not produce an amount equal to 7/6 of the principal in 3 years under simple interest. Substituting any of these into the formula SI = (P * r * 3) / 100 gives a fraction of P different from 1/6. Hence, they are not consistent with the given condition.

Common Pitfalls:
Students sometimes miscalculate the difference between 7/6 and 1, or they forget to cancel the principal P before solving for r. Others incorrectly manipulate fractions when dividing by 3 and 100. Careful fraction handling and stepwise algebra help avoid these errors.

Final Answer:
The rate of interest per annum is 50/9%.