Q 42. Aman and Ravi appeared for a mathematics test. Aman scored 24 marks more than Ravi, and his marks were 60% of their combined total. How many marks did Aman score?
01) 48
02) 72
03) 54
04) 88

Let the marks scored by Ravi be \( x \). 

According to the problem, Aman scored 24 marks more than Ravi, so Aman's marks would be \( x + 24 \).

The problem also states that Aman's marks are 60% of their combined total. The combined total of their marks is \( x + (x + 24) = 2x + 24 \).

Now, we can set up the equation using the 60% condition:

\[
x + 24 = 0.60 \times (2x + 24)
\]

Simplifying this equation:

\[
x + 24 = 0.60(2x + 24)
\]
\[
x + 24 = 1.2x + 14.4
\]
\[
x + 24 - 1.2x = 14.4
\]
\[
-0.2x + 24 = 14.4
\]
\[
-0.2x = 14.4 - 24
\]
\[
-0.2x = -9.6
\]
\[
x = \frac{-9.6}{-0.2} = 48
\]

So, Ravi scored 48 marks, and Aman's marks are:

\[
x + 24 = 48 + 24 = 72
\]

Thus, Aman scored **72 marks**. The correct answer is:

\[
\boxed{72}
\]

Would you like more details on any step, or do you have further questions? Here are some related questions:

1. How would the equation change if Aman scored 30 marks more than Ravi?
2. What if Aman's marks were 70% of their combined total?
3. Can you solve a similar problem where Aman scored 20 marks more than Ravi?
4. How does the solution change if Aman's marks were 50% of the total?
5. What happens if Ravi scored 60 marks in the test instead?

**Tip:** When forming equations from word problems, translate the conditions step-by-step into mathematical expressions.

Aman and Ravi appeared for a mathematics test. Aman scored 24 marks more than Ravi, and his marks were 60% of their combined total. How many marks did Aman score?

Learn how to solve a problem where Aman scores 24 marks more than Ravi and his score is 60% of their combined total. This step-by-step solution involves key algebraic concepts, including solving linear equations and working with percentages. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation