Directions: These questions are based on the following information: In a holy city, there are ten shrines and a certain number of holy lakes. A group of pilgrims stayed in the city for a few days and visited the shrines and lakes during their stay. At the end of the stay it turned out that in all each shrine was visited exactly by $4$ pilgrims and each lake was visited exactly by $6$ pilgrims. Each pilgrim visited exactly $5$ shrines and $3$ lakes. The number of pilgrims in the group is

Concept & Logic The core concept relies on equating the total volume of an activity calculated from two different perspectives. The total number of shrine visits counted by looking at the shrines must equal the total number of shrine visits counted by looking at the pilgrims. Step-by-Step Solution * **Given Information:** Number of shrines = $10$ Visits per shrine = $4$ pilgrims Shrine visits per pilgrim = $5$ * **Calculation / Deduction:** Calculate the total number of times any shrine was entered. Total Shrine Visits = (Number of Shrines) $\times$ (Pilgrims per Shrine) Total Shrine Visits = $10 \times 4 = 40$ Now, look at this from the pilgrims' side. Let the number of pilgrims be $P$. Total Shrine Visits = (Number of Pilgrims) $\times$ (Shrines per Pilgrim) $40 = P \times 5$ Solve for $P$: $P = \frac{40}{5} = 8$ Exam Strategy & Shortcut For data sets with common directions, always solve the easiest and most direct variable first. Here, the complete data exists for shrines. Mental math: $10 \times 4 = 40$, divided by $5$ equals $8$. You don't even need to write anything down. Common Pitfall Students might get distracted by the "lakes" information in the prompt. For this specific question, the lake data is completely irrelevant "noise". Don't feel obligated to use every number in a word problem if a direct path exists. Final Answer Therefore, the correct answer is **8**.