In a test Abha gets twice the marks as that of Palak. Two times Abha.s marks and three times Palak.s marks make 280.
If Palak gets x marks, Abha gets ________marks.

Options

A. 80
B. 40
C. 60
D. 100

Answer

To solve the problem step by step, we will follow the given information and derive the necessary equations.

### Step 1: Define the variables
Let Palak's marks be represented by \( x \).

### Step 2: Express Abha's marks in terms of \( x \)
According to the problem, Abha gets twice the marks of Palak. Therefore, we can express Abha's marks as:
\[ \text{Abha's marks} = 2x \]

### Step 3: Set up the equation based on the second condition
The problem states that two times Abha's marks and three times Palak's marks equal 280. We can write this as:
\[ 2 \times (\text{Abha's marks}) + 3 \times (\text{Palak's marks}) = 280 \]
Substituting the expressions we have:
\[ 2 \times (2x) + 3 \times (x) = 280 \]

### Step 4: Simplify the equation
Now, simplify the left side of the equation:
\[ 4x + 3x = 280 \]
Combine like terms:
\[ 7x = 280 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 7:
\[ x = \frac{280}{7} \]
Calculating this gives:
\[ x = 40 \]

### Step 6: Calculate Abha's marks
Now that we have the value of \( x \), we can find Abha's marks:
\[ \text{Abha's marks} = 2x = 2 \times 40 \]
Calculating this gives:
\[ \text{Abha's marks} = 80 \]

### Final Answer
Abha gets **80 marks**.

---