The ratio of marks obtained by a student in 3 subject was `1:2:3`. The teacher decided to allow grace marks of 5% for each subject. Find the student' s new ratio.

Options

A. a. `1:2:3`
B. b. `2:3:4`
C. c. `2:3:1`
D. d. `3:2:1`

Answer

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

### Step 1: Understand the given ratio of marks
The ratio of marks obtained by the student in three subjects is given as \(1:2:3\).

### Step 2: Assign values to the marks
To make calculations easier, we can assign actual marks based on the ratio. Let's assume:
- Marks in subject 1 = \(1x\)
- Marks in subject 2 = \(2x\)
- Marks in subject 3 = \(3x\)

### Step 3: Calculate the grace marks
The teacher allows a grace of 5% for each subject. We will calculate the new marks after adding the grace marks.

- For subject 1:
\[ \text{New marks} = 1x + 0.05 \times 1x = 1x + 0.05x = 1.05x \]

- For subject 2:
\[ \text{New marks} = 2x + 0.05 \times 2x = 2x + 0.1x = 2.1x \]

- For subject 3:
\[ \text{New marks} = 3x + 0.05 \times 3x = 3x + 0.15x = 3.15x \]

### Step 4: Write the new marks
Now, we have the new marks as:
- Subject 1: \(1.05x\)
- Subject 2: \(2.1x\)
- Subject 3: \(3.15x\)

### Step 5: Find the new ratio
To find the new ratio, we will express the new marks in the simplest form:
\[ \text{New ratio} = 1.05x : 2.1x : 3.15x \]
We can cancel \(x\) from all terms:
\[ \text{New ratio} = 1.05 : 2.1 : 3.15 \]

### Step 6: Simplify the new ratio
To simplify \(1.05 : 2.1 : 3.15\), we can convert these decimals to fractions or multiply by 100 to eliminate decimals:
\[ \text{New ratio} = 105 : 210 : 315 \]

Now, we can simplify this ratio by dividing each term by 105:
\[ \text{New ratio} = 1 : 2 : 3 \]

### Final Answer
The new ratio of marks obtained by the student after adding grace marks is \(1:2:3\).