Two students appeared in an examination, in which the first student scored 102) 12 more than the second student and his marks are 60% of the sum of both the marks, then he obtained

Let's denote the marks of the two students as follows:
- Let \( x \) be the marks of the second student.
- The marks of the first student are then \( x + 12 \), as the problem states that the first student scored 12 more than the second.

It is also given that the first student's marks are 60% of the sum of both their marks. Mathematically, we can write this as:

\[
x + 12 = 0.60 \times (x + (x + 12))
\]

Now, let's solve this equation step by step:

### Step 1: Simplify the equation.
\[
x + 12 = 0.60 \times (2x + 12)
\]
\[
x + 12 = 1.2x + 7.2
\]

### Step 2: Rearrange the terms to isolate \(x\).
\[
x - 1.2x = 7.2 - 12
\]
\[
-0.2x = -4.8
\]

### Step 3: Solve for \(x\).
\[
x = \frac{-4.8}{-0.2} = 24
\]

So, the second student scored **24 marks**.

### Step 4: Calculate the first student's marks.
\[
x + 12 = 24 + 12 = 36
\]

Thus, the first student obtained **36 marks**.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions:
1. What is the sum of the marks of both students?
2. What percentage of the total marks did the second student score?
3. How would the result change if the first student scored 15 more than the second?
4. What if the first student scored 50% of the total instead of 60%?
5. Can you express the marks as a ratio between the two students?

**Tip**: Always double-check your percentage conversions in word problems to avoid errors.

Two students appeared in an examination, in which the first student scored 12 more than the second student and his marks are 60% of the sum of both the marks, then he obtained.

This problem involves determining the marks of two students where one student's score is 12 more than the other, and his score represents 60% of their combined total. Learn how to solve this step-by-step using algebraic methods, perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation