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
Out of the total number of domestic travellers (male+ female) in January and February together, the ratio of the number of male domestic travellers to that of female domestic travellers is 1: 5. What is the total number of male domestic travellers in January and February together?

Options

A. 1675
B. 385
C. 1825
D. 750

Answer

To solve the problem step-by-step, let's break down the information given and derive the required values systematically.

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

### Step 2: Calculate Domestic Travellers
From the problem, we know that:
- In January, domestic travellers = \(\frac{4}{5}\) of total travellers in January
\[ \text{Domestic travellers in January} = \frac{4}{5} \times 2x = \frac{8x}{5} \]
- In February, domestic travellers = \(\frac{3}{4}\) of total travellers in February
\[ \text{Domestic travellers in February} = \frac{3}{4} \times 3x = \frac{9x}{4} \]

### Step 3: Total Domestic Travellers
Now, we can find the total number of domestic travellers in January and February:
\[ \text{Total domestic travellers} = \frac{8x}{5} + \frac{9x}{4} \]
To add these fractions, we need a common denominator:
\[ \text{Common denominator} = 20 \]
Thus,
\[ \frac{8x}{5} = \frac{32x}{20}, \quad \frac{9x}{4} = \frac{45x}{20} \]
Adding them gives:
\[ \text{Total domestic travellers} = \frac{32x + 45x}{20} = \frac{77x}{20} \]

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

### Step 5: Travellers in April
The total number of travellers in April is twice that in March:
\[ \text{Total travellers in April} = 2 \times \frac{9x}{4} = \frac{18x}{4} = \frac{9x}{2} \]

### Step 6: Domestic Travellers in March
We know from the problem that there are 1215 domestic travellers in March:
\[ \text{Domestic travellers in March} = 1215 \]

### Step 7: International Travellers in March
The number of international travellers in March is 315 less than that in February. Let’s denote the international travellers in February as \(I_F\):
\[ I_M = I_F - 315 \]
From the total number of travellers in February:
\[ I_F + \frac{9x}{4} = 3x \implies I_F = 3x - \frac{9x}{4} = \frac{12x - 9x}{4} = \frac{3x}{4} \]
Thus,
\[ I_M = \frac{3x}{4} - 315 \]

### Step 8: Set Up the Equation
From the total travellers in March:
\[ \text{Total in March} = I_M + 1215 \]
Substituting for \(I_M\):
\[ \frac{9x}{4} = \left(\frac{3x}{4} - 315\right) + 1215 \]
Simplifying:
\[ \frac{9x}{4} = \frac{3x}{4} + 900 \implies \frac{9x - 3x}{4} = 900 \implies \frac{6x}{4} = 900 \implies 6x = 3600 \implies x = 600 \]

### Step 9: Calculate Domestic Travellers in January and February
Now substituting \(x = 600\):
- Domestic travellers in January:
\[ \frac{8x}{5} = \frac{8 \times 600}{5} = 960 \]
- Domestic travellers in February:
\[ \frac{9x}{4} = \frac{9 \times 600}{4} = 1350 \]
Total domestic travellers in January and February:
\[ 960 + 1350 = 2310 \]

### Step 10: Calculate Male Domestic Travellers
Given the ratio of male to female domestic travellers is \(1:5\), let the number of male domestic travellers be \(x\) and female be \(5x\):
\[ x + 5x = 2310 \implies 6x = 2310 \implies x = 385 \]

### Final Answer
The total number of male domestic travellers in January and February together is:
\[ \boxed{385} \]