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

Answer: (C)

60

Answer 2

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.