In a university the number of stu dents studying science, mathe matics and language is in the re spective ratio of 2:4:9. If the number of students of science, mathematics and language is in creased by 10%, 20% and 40% respectively, what will be the new ratio?

Options

A. A) `63:11:24`
B. B) `12:23:63`
C. C) `24:11:63`
D. D) `11:24:63`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given ratio
The number of students studying science, mathematics, and language is in the ratio of 2:4:9.

### Step 2: Assign variables based on the ratio
Let the number of students studying science be \(2x\), mathematics be \(4x\), and language be \(9x\), where \(x\) is a common multiplier.

### Step 3: Calculate the initial number of students
To make calculations easier, we can assume \(x = 100\) (this is just for convenience):
- Science: \(2x = 2 \times 100 = 200\)
- Mathematics: \(4x = 4 \times 100 = 400\)
- Language: \(9x = 9 \times 100 = 900\)

### Step 4: Calculate the increase in the number of students
Now, we will calculate the increased number of students based on the given percentages:
- Science: Increased by 10%
\[ \text{New number of Science students} = 200 + (10\% \text{ of } 200) = 200 + 20 = 220 \]

- Mathematics: Increased by 20%
\[ \text{New number of Mathematics students} = 400 + (20\% \text{ of } 400) = 400 + 80 = 480 \]

- Language: Increased by 40%
\[ \text{New number of Language students} = 900 + (40\% \text{ of } 900) = 900 + 360 = 1260 \]

### Step 5: Write the new numbers in ratio form
Now we have the new numbers of students:
- Science: 220
- Mathematics: 480
- Language: 1260

The new ratio of students studying science, mathematics, and language is:
\[ 220 : 480 : 1260 \]

### Step 6: Simplify the ratio
To simplify the ratio, we can divide each term by 20 (the greatest common divisor):
\[ \frac{220}{20} : \frac{480}{20} : \frac{1260}{20} = 11 : 24 : 63 \]

### Final Answer
The new ratio of students studying science, mathematics, and language is:
\[ \boxed{11 : 24 : 63} \]

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