Math Problem Statement

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

Solution

Let the marks scored by Ravi be xx.

According to the problem, Aman scored 24 marks more than Ravi, so Aman's marks would be x+24x + 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+24x + (x + 24) = 2x + 24.

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

x+24=0.60×(2x+24)x + 24 = 0.60 \times (2x + 24)

Simplifying this equation:

x+24=0.60(2x+24)x + 24 = 0.60(2x + 24) x+24=1.2x+14.4x + 24 = 1.2x + 14.4 x+241.2x=14.4x + 24 - 1.2x = 14.4 0.2x+24=14.4-0.2x + 24 = 14.4 0.2x=14.424-0.2x = 14.4 - 24 0.2x=9.6-0.2x = -9.6 x=9.60.2=48x = \frac{-9.6}{-0.2} = 48

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

x+24=48+24=72x + 24 = 48 + 24 = 72

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

72\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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentages
Linear Equations

Formulas

x + 24 = 0.60 * (2x + 24)
Solving linear equations

Theorems

None (basic algebraic manipulation)

Suitable Grade Level

Grades 6-8