Weighted month in annual income: Ravi earns exactly twice as much in January as he earns in each of the other months of the year. What fraction of his total annual earnings does he earn in January?

Introduction / Context:
This question tests the ability to convert a proportional monthly statement into a fraction of an annual total. It uses uniform earnings across months except for one weighted month (January).

Given Data / Assumptions:

• Let earnings in each non-January month be k.
• January earnings are 2k.
• There are 12 months in total.

Concept / Approach:
Compute total annual income as the sum of 11 months at k plus January at 2k. Then express January’s income as a fraction of the total and reduce to lowest terms.

Step-by-Step Solution:
Total annual = 11*k + 2k = 13k.January share = 2k.Required fraction = January / Total = 2k / 13k = 2/13.

Verification / Alternative check:
Pick any k (e.g., k = 1). Then January = 2, yearly total = 13, so January is 2/13 of the annual income, independent of k.

Why Other Options Are Wrong:
1/10, 1/5, 1/6 do not reflect the 13k total; 5/7 is unrelated to the 12-month structure with a single doubled month.

Common Pitfalls:
Forgetting there are 11 non-January months; adding an extra month; reducing 2/13 incorrectly.

Final Answer:
2/13