If a time duration is described as k weeks and k days, how many total days does this period contain in terms of k?

Introduction / Context:
This question checks a very basic but important skill in aptitude and arithmetic: converting weeks and days into an equivalent total number of days. Expressing the result in terms of a variable k also tests your understanding of algebraic representation. Such problems often appear in time and work, time and distance, and calendar topics.

Given Data / Assumptions:

• The duration is given as k weeks and k days.
• We know that 1 week is equal to 7 days.
• k is a positive integer representing a number of weeks and days.
• We need to express the total duration purely in days, using k.

Concept / Approach:
The approach is straightforward unit conversion. First convert the weeks part into days using 1 week = 7 days. Then add the extra days given separately. Finally, simplify the algebraic expression. The key idea is to treat k as a symbol and keep it attached consistently in every term.

Step-by-Step Solution:
Step 1: Start with k weeks. Since 1 week = 7 days, k weeks = 7 * k days. Step 2: The description also includes an additional k days. Step 3: Total days = days from weeks + extra days = 7k + k. Step 4: Factor out k from both terms: 7k + k = (7 + 1)k. Step 5: Simplify (7 + 1)k = 8k. Step 6: Therefore the total number of days is 8k days.

Verification / Alternative check:
To verify, plug in a simple value for k. For example, let k = 2. Then the duration is 2 weeks and 2 days. Two weeks are 14 days, plus 2 more days gives 16 days. The expression 8k gives 8 * 2 = 16, which matches perfectly. This confirms that the formula is consistent for at least one test value and the reasoning is correct.

Why Other Options Are Wrong:
8 + k days: This mixes a constant with k and does not reflect the effect of k weeks properly because weeks grow with k.
7 + 1k days: This again treats only one part linearly in k and ignores that the weeks part already contributes 7k days.
7/k days: This divides instead of multiplies and is dimensionally inconsistent with the idea of weeks growing with k.

Common Pitfalls:
Students sometimes misread k weeks k days as something like k weeks plus 1 day, or they forget to multiply weeks by 7. Another common error is writing 7k + 1k but then simplifying incorrectly. Always keep in mind that a variable like k behaves like a normal number during multiplication and addition, so expressions can and should be simplified.

Final Answer:
The total number of days in k weeks and k days is 8k days.