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 lakes in the holy city is

Concept & Logic The problem can be solved using the principle of **Total Engagements** or **Total Visits**. The total number of visits to shrines calculated from the shrines' perspective must perfectly equal the total number of visits calculated from the pilgrims' perspective. Step-by-Step Solution * **Total Shrine Visits (Shrines' Perspective):** There are $10$ shrines. Each was visited by exactly $4$ pilgrims. Total visits = $10 \times 4 = 40$ visits. * **Finding the Number of Pilgrims:** Let the total number of pilgrims be $P$. Each pilgrim visits exactly $5$ shrines. Total visits = $P \times 5$. Equating the two: $5P = 40 \Rightarrow P = 8$. There are $8$ pilgrims in total. * **Total Lake Visits (Pilgrims' Perspective):** There are $8$ pilgrims, and each visits exactly $3$ lakes. Total lake visits = $8 \times 3 = 24$ visits. * **Finding the Number of Lakes:** Let the number of lakes be $L$. Each lake is visited by exactly $6$ pilgrims. Total lake visits = $L \times 6$. Equating the two: $6L = 24 \Rightarrow L = 4$. Exam Strategy & Shortcut Break complex puzzle paragraphs into independent conservation equations. Total Item Capacity = Total People Consumption. Solve for people first using the fully known parameter (shrines), then immediately plug that into the unknown parameter (lakes) to find the answer in under 30 seconds. Common Pitfall A major mistake is trying to solve for lakes and pilgrims simultaneously using a complex system of equations, getting lost in variables. Recognize that the "shrine" data is complete and independently solvable. Solve sequentially. Final Answer Therefore, the correct answer is **4**.