Question

At a dinner party, every two guests used a dish of rice between them. Every three guests used a dish of daal and every four used a dish of meat between them. There were altogether 65 dishes. How many guests were present?

• A. 75
• B. 59
• C. 60
• D. 65

Answer 1

The Correct Option is C

The correct option is (C): 60
Let's assume the number of guests present is \( n \).

Step 1: Analyze the use of dishes
- Dishes of rice: Every two guests share a dish of rice, so the number of rice dishes is \( \frac{n}{2} \).
- Dishes of daal: Every three guests share a dish of daal, so the number of daal dishes is \( \frac{n}{3} \).
- Dishes of meat: Every four guests share a dish of meat, so the number of meat dishes is \( \frac{n}{4} \).

Step 2: Total number of dishes
We are told the total number of dishes is 65, so:
\[\frac{n}{2} + \frac{n}{3} + \frac{n}{4} = 65\]

Step 3: Find the common denominator and simplify
The least common denominator for 2, 3, and 4 is 12. So, rewriting the equation:
\[\frac{6n}{12} + \frac{4n}{12} + \frac{3n}{12} = 65\]
Simplifying:
\[\frac{13n}{12} = 65\]

Step 4: Solve for \( n \)
Multiplying both sides by 12 to eliminate the fraction:
\[13n = 65 \times 12 = 780\]
Now, divide by 13:
\[n = \frac{780}{13} = 60\]

Final Answer:
The number of guests present is 60.