Two students appeared for an examination. One student who scored 20 marks more than the other, his score was 60% of the sum of their marks. What was his score?

Options

A. 80
B. 20
C. 40
D. 60

Answer

To solve the problem step by step, we will denote the scores of the two students as follows:

1. Let the score of the first student be \( x \).
2. Since the second student scored 20 marks more than the first, his score will be \( x + 20 \).

Now, according to the problem, the score of the second student is also 60% of the sum of their scores. The sum of their scores can be calculated as:

\[ \text{Sum of scores} = x + (x + 20) = 2x + 20 \]

Now, we can express the condition given in the problem mathematically:

\[ x + 20 = 0.6 \times (2x + 20) \]

Next, we will simplify the equation:

1. Expand the right side:
\[ x + 20 = 0.6 \times 2x + 0.6 \times 20 \]
\[ x + 20 = 1.2x + 12 \]

2. Rearranging the equation to isolate \( x \):
\[ x + 20 - 12 = 1.2x \]
\[ x + 8 = 1.2x \]

3. Subtract \( x \) from both sides:
\[ 8 = 1.2x - x \]
\[ 8 = 0.2x \]

4. Now, solve for \( x \):
\[ x = \frac{8}{0.2} = 40 \]

Now that we have the score of the first student, we can find the score of the second student:

\[ \text{Score of the second student} = x + 20 = 40 + 20 = 60 \]

Thus, the score of the second student is **60**.

### Summary of Steps:
1. Let the first student's score be \( x \) and the second student's score be \( x + 20 \).
2. Set up the equation based on the condition given in the problem.
3. Simplify the equation to isolate \( x \).
4. Solve for \( x \) to find the score of the first student.
5. Calculate the score of the second student.