Rohit scores 84 in Maths while 79 in Science. Karan scores 85 in Maths. If average score of Karan is 6 more than average score of Rohit in both the subjects. Find the marks scored by Karan in Science.

Options

A. A)90
B. B)85
C. C)87.5
D. D)81.5

Answer

To solve the problem step by step, we need to find the marks scored by Karan in Science. Let's break it down:

### Step 1: Calculate Rohit's Average Score
Rohit scores:
- Maths: 84
- Science: 79

To find Rohit's average score in both subjects, we use the formula for average:

\[ \text{Average Score of Rohit} = \frac{\text{Maths Score} + \text{Science Score}}{2} \]

Substituting in the values:

\[ \text{Average Score of Rohit} = \frac{84 + 79}{2} = \frac{163}{2} = 81.5 \]

### Step 2: Set Up the Equation for Karan's Average Score
Karan scores:
- Maths: 85
- Science: Let’s denote Karan's score in Science as \( Y \).

Karan's average score is given by:

\[ \text{Average Score of Karan} = \frac{85 + Y}{2} \]

### Step 3: Relate Karan's Average to Rohit's Average
According to the problem, Karan's average score is 6 more than Rohit's average score. Therefore, we can write:

\[ \frac{85 + Y}{2} = 81.5 + 6 \]

Calculating the right side:

\[ 81.5 + 6 = 87.5 \]

So, we have:

\[ \frac{85 + Y}{2} = 87.5 \]

### Step 4: Solve for \( Y \)
Now, we will multiply both sides of the equation by 2 to eliminate the fraction:

\[ 85 + Y = 87.5 \times 2 \]

Calculating the right side:

\[ 87.5 \times 2 = 175 \]

So, we have:

\[ 85 + Y = 175 \]

Now, subtract 85 from both sides to find \( Y \):

\[ Y = 175 - 85 \]
\[ Y = 90 \]

### Conclusion
Karan's score in Science is \( 90 \).