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
The number of international travellers in March is what per cent less than that in January?

Options

A. 50
B. 43.75
C. 36.8
D. 32

Answer

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

### Step 1: Define Variables
Let the total number of travellers in February be \( 3x \).
Then, the total number of travellers in January will be \( \frac{2}{3} \times 3x = 2x \).

### Step 2: Calculate Domestic Travellers
According to the problem:
- In January, \( \frac{4}{5} \) of the total travellers are domestic.
- In February, \( \frac{3}{4} \) of the total travellers are domestic.

So, we can calculate:
- Domestic travellers in January = \( \frac{4}{5} \times 2x = \frac{8x}{5} \)
- Domestic travellers in February = \( \frac{3}{4} \times 3x = \frac{9x}{4} \)

### Step 3: Relate March and February
The total number of travellers in March is equal to the number of domestic travellers in February, which is \( \frac{9x}{4} \).

### Step 4: Calculate April Travellers
The total number of travellers in April is twice that in March:
- Total travellers in April = \( 2 \times \frac{9x}{4} = \frac{18x}{4} = \frac{9x}{2} \)

### Step 5: Domestic and International Travellers in March
We know that there are 1215 domestic travellers in March. Therefore:
- Domestic travellers in March = 1215
- International travellers in March = Total travellers in March - Domestic travellers in March = \( \frac{9x}{4} - 1215 \)

### Step 6: International Travellers in February
The number of international travellers in March is 315 less than that in February. Let:
- International travellers in February = \( \frac{3x}{4} \)
- International travellers in March = \( \frac{3x}{4} - 315 \)

### Step 7: Set Up the Equation
From the above information, we can set up the equation:
\[ \frac{9x}{4} - 1215 = \frac{3x}{4} - 315 \]

### Step 8: Solve for x
Rearranging the equation:
\[ \frac{9x}{4} - \frac{3x}{4} = 1215 - 315 \]
\[ \frac{6x}{4} = 900 \]
\[ 6x = 3600 \]
\[ x = 600 \]

### Step 9: Calculate Total Travellers
Now we can calculate the total number of travellers in each month:
- February: \( 3x = 3 \times 600 = 1800 \)
- January: \( 2x = 1200 \)
- March: \( \frac{9x}{4} = \frac{9 \times 600}{4} = 1350 \)
- April: \( \frac{9x}{2} = \frac{9 \times 600}{2} = 2700 \)

### Step 10: Calculate International Travellers
Now we can calculate the number of international travellers:
- International travellers in February = \( \frac{3x}{4} = \frac{3 \times 600}{4} = 450 \)
- International travellers in March = \( 450 - 315 = 135 \)

### Step 11: International Travellers in January
International travellers in January:
- \( \text{Total in January} - \text{Domestic in January} = 1200 - \frac{8x}{5} = 1200 - 960 = 240 \)

### Step 12: Calculate Percentage Decrease
Now, we need to find the percentage decrease of international travellers in March compared to January:
\[ \text{Decrease} = 240 - 135 = 105 \]
\[ \text{Percentage decrease} = \left( \frac{105}{240} \right) \times 100 = 43.75\% \]

### Final Answer
The number of international travellers in March is **43.75% less** than that in January.

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