One-third of Karan's marks in Science exceeds a half of his marks in Hindi by 30. If he got 240 marks in the two subjects together, then how many marks did he get in Hindi?

Options

A. 42
B. 50
C. 60
D. 180

Answer

Let's solve the problem step by step.

**Step 1: Define the variables.**
Let Karan's marks in Science be \( S \) and his marks in Hindi be \( H \).

**Step 2: Set up the equations based on the problem statement.**
According to the problem, one-third of Karan's marks in Science exceeds half of his marks in Hindi by 30. This can be expressed as:
\[ \frac{1}{3}S = \frac{1}{2}H + 30 \]

**Step 3: Set up the second equation based on the total marks.**
We know that Karan got a total of 240 marks in both subjects. Therefore, we can write:
\[ S + H = 240 \]

**Step 4: Solve the equations.**
We have two equations now:
1. \( \frac{1}{3}S = \frac{1}{2}H + 30 \)
2. \( S + H = 240 \)

From the second equation, we can express \( S \) in terms of \( H \):
\[ S = 240 - H \]

**Step 5: Substitute \( S \) in the first equation.**
Now substitute \( S \) in the first equation:
\[ \frac{1}{3}(240 - H) = \frac{1}{2}H + 30 \]

**Step 6: Multiply through by 6 to eliminate the fractions.**
Multiplying the entire equation by 6 gives:
\[ 2(240 - H) = 3H + 180 \]

**Step 7: Distribute and simplify.**
Distributing on the left side:
\[ 480 - 2H = 3H + 180 \]

**Step 8: Combine like terms.**
Now, add \( 2H \) to both sides:
\[ 480 = 5H + 180 \]
Subtract 180 from both sides:
\[ 300 = 5H \]

**Step 9: Solve for \( H \).**
Now divide both sides by 5:
\[ H = 60 \]

**Step 10: Find \( S \) using \( H \).**
Now that we have \( H \), we can find \( S \):
\[ S = 240 - H = 240 - 60 = 180 \]

**Final Answer:**
Karan got **60 marks in Hindi**.

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