Study the following information carefully to answer the given questions
The data is regarding the number of travellers handled by a travel and tour company in four months (January, February, March and April) of a year.
Note: The total number of travellers (male + female) =international (male + female) + domestic (male + female)
The total number of travellers in January is `2/3` of that in February
`4/5`and `3/4` of the total number of travellers in January and February, respectively, are domestic travellers. The total number of travellers in March is equal to the number of domestic travellers in February. The total number of travellers in April is twice that in March.
There are 1215 domestic travellers in March and the number of international travellers in March is 315 less than that in February.
The number of international travellers in April is `1/3` of that in February

In December in the same year, the total number of travellers grew by `60%` from that in March. If `30%` of the total number of travellers are international travellers, then how many international travellers were handled by the company in December?

Options

A. 540
B. 442
C. 670
D. 648

Answer

To solve the problem step-by-step, we will analyze the information given about the number of travelers handled by the travel and tour company in the months of January, February, March, and April.

### Step 1: Define Variables
Let the total number of travelers in February be \(3x\). According to the problem, the total number of travelers in January is \( \frac{2}{3} \) of that in February. Therefore, the total number of travelers in January will be:
\[ \text{Total travelers in January} = \frac{2}{3} \times 3x = 2x \]

### Step 2: Determine Domestic Travelers
From the information provided:
- In January, \( \frac{4}{5} \) of the total travelers are domestic. Thus, the number of domestic travelers in January is:
\[ \text{Domestic travelers in January} = \frac{4}{5} \times 2x = \frac{8x}{5} \]

- In February, \( \frac{3}{4} \) of the total travelers are domestic. Thus, the number of domestic travelers in February is:
\[ \text{Domestic travelers in February} = \frac{3}{4} \times 3x = \frac{9x}{4} \]

### Step 3: Total Travelers in March
The total number of travelers in March is equal to the number of domestic travelers in February:
\[ \text{Total travelers in March} = \frac{9x}{4} \]

### Step 4: Total Travelers in April
The total number of travelers in April is twice that in March:
\[ \text{Total travelers in April} = 2 \times \frac{9x}{4} = \frac{9x}{2} \]

### Step 5: Determine Domestic Travelers in March
We are told that there are 1215 domestic travelers in March. Therefore:
\[ \frac{9x}{4} = 1215 \]
To find \(x\):
\[ 9x = 1215 \times 4 \\ 9x = 4860 \\ x = \frac{4860}{9} = 540 \]

### Step 6: Calculate Total Travelers in Each Month
Now that we have \(x\), we can calculate the total travelers for each month:
- Total travelers in February:
\[ 3x = 3 \times 540 = 1620 \]
- Total travelers in January:
\[ 2x = 2 \times 540 = 1080 \]
- Total travelers in March:
\[ \frac{9x}{4} = \frac{9 \times 540}{4} = 1215 \]
- Total travelers in April:
\[ \frac{9x}{2} = \frac{9 \times 540}{2} = 2430 \]

### Step 7: Determine International Travelers
The number of international travelers in March is given as 315 less than that in February. First, we calculate the international travelers in February:
\[ \text{International travelers in February} = 1620 - \frac{9x}{4} = 1620 - 1215 = 405 \]
Thus, the international travelers in March:
\[ \text{International travelers in March} = 405 - 315 = 90 \]

### Step 8: Calculate International Travelers in April
The number of international travelers in April is \( \frac{1}{3} \) of that in February:
\[ \text{International travelers in April} = \frac{1}{3} \times 405 = 135 \]

### Step 9: Calculate Total Travelers in December
The total number of travelers in December is a 60% increase from that in March:
\[ \text{Total travelers in December} = \frac{9x}{4} \times 160\% = 1215 \times 1.6 = 1944 \]

### Step 10: Calculate International Travelers in December
30% of the total travelers in December are international travelers:
\[ \text{International travelers in December} = 0.3 \times 1944 = 583.2 \]
Since the number of travelers must be a whole number, we round it to 583.

### Final Answer
The number of international travelers handled by the company in December is **583**.