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
What is the difference between the total number of travellers in February and that in April?

Options

A. 800
B. 900
C. 600
D. 720

Answer

To solve the problem step by step, let's break down the information provided and calculate the required values.

### Step 1: Define Variables
Let the total number of travellers in February be represented as \(3x\). According to the problem, the total number of travellers in January is \( \frac{2}{3} \) of that in February, which means:
- Total travellers in January = \(2x\)

### Step 2: Calculate Domestic Travellers
From the information given:
- \( \frac{4}{5} \) of the total travellers in January are domestic:
- Domestic travellers in January = \( \frac{4}{5} \times 2x = \frac{8x}{5} \)

- \( \frac{3}{4} \) of the total travellers in February are domestic:
- Domestic travellers in February = \( \frac{3}{4} \times 3x = \frac{9x}{4} \)

### Step 3: Total Travellers in March
The total number of travellers in March is equal to the number of domestic travellers in February, which we calculated as:
- Total travellers in March = \( \frac{9x}{4} \)

### Step 4: Total Travellers in April
The total number of travellers in April is twice that in March:
- Total travellers in April = \( 2 \times \frac{9x}{4} = \frac{9x}{2} \)

### Step 5: Domestic Travellers in March
It is given that there are 1215 domestic travellers in March. Therefore:
- Domestic travellers in March = 1215

### Step 6: 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 \( I_F \) and in March as \( I_M \):
- \( I_M = I_F - 315 \)

### Step 7: Calculate International Travellers
From the total in March:
- Total travellers in March = Domestic + International
- \( \frac{9x}{4} = 1215 + (I_F - 315) \)

Rearranging gives:
- \( \frac{9x}{4} = 1215 + I_F - 315 \)
- \( \frac{9x}{4} = I_F + 900 \)

### Step 8: International Travellers in February
Now, we also know:
- Domestic travellers in February = \( \frac{9x}{4} \)
- Total travellers in February = \( 3x \)
- Therefore, \( I_F = 3x - \frac{9x}{4} = \frac{12x - 9x}{4} = \frac{3x}{4} \)

### Step 9: Substitute and Solve for x
Substituting \( I_F \) into the equation:
- \( \frac{9x}{4} = \frac{3x}{4} + 900 \)
- Rearranging gives:
- \( \frac{9x}{4} - \frac{3x}{4} = 900 \)
- \( \frac{6x}{4} = 900 \)
- \( 6x = 3600 \)
- \( x = 600 \)

### Step 10: Calculate Total Travellers
Now that we have \( x \):
- Total travellers in February = \( 3x = 3 \times 600 = 1800 \)
- Total travellers in April = \( \frac{9x}{2} = \frac{9 \times 600}{2} = 2700 \)

### Step 11: Find the Difference
The difference between the total number of travellers in February and April:
- Difference = Total in April - Total in February
- Difference = \( 2700 - 1800 = 900 \)

### Final Answer
The difference between the total number of travellers in February and that in April is **900**.

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