Sunny gets `3(1)/2` times as many marks in 'QA' as he gets in 'English'. If his total combined marks in both the papers is 90. His marks in 'QA' is :

Options

A. 50
B. 60
C. 70
D. none of these

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the marks Sunny gets in 'English' be represented by \( X \).

### Step 2: Express Marks in 'QA'
According to the problem, Sunny gets \( 3\frac{1}{2} \) times as many marks in 'QA' as he gets in 'English'. We can convert \( 3\frac{1}{2} \) into an improper fraction:
\[ 3\frac{1}{2} = \frac{7}{2} \]
Thus, the marks in 'QA' can be expressed as:
\[ \text{Marks in QA} = \frac{7}{2}X \]

### Step 3: Set Up the Equation
The total combined marks in both subjects is given as 90. Therefore, we can set up the equation:
\[ X + \frac{7}{2}X = 90 \]

### Step 4: Combine Like Terms
To combine the terms on the left side, we need a common denominator. The common denominator for \( 1X \) (which is \( \frac{2}{2}X \)) and \( \frac{7}{2}X \) is 2:
\[ \frac{2}{2}X + \frac{7}{2}X = \frac{2X + 7X}{2} = \frac{9X}{2} \]
So, the equation becomes:
\[ \frac{9X}{2} = 90 \]

### Step 5: Solve for \( X \)
To eliminate the fraction, multiply both sides of the equation by 2:
\[ 9X = 180 \]
Now, divide both sides by 9:
\[ X = 20 \]

### Step 6: Calculate Marks in 'QA'
Now that we have the value of \( X \), we can find the marks in 'QA':
\[ \text{Marks in QA} = \frac{7}{2}X = \frac{7}{2} \times 20 = 70 \]

### Final Answer
Sunny's marks in 'QA' is \( 70 \).

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