Question

The ratio of four numbers is 3 : 4 : 5 : 6 and the sum of the four numbers is 7200. The largest of the four numbers, is

• A. 2800
• B. 2600
• C. 3200
• D. 2400

Hint:

To quickly solve ratio partition questions, sum up the ratio parts: \(3 + 4 + 5 + 6 = 18\) parts.
Divide the total value by the total parts: \(7200 / 18 = 400\) (value per part).
Multiply this single part value by the largest ratio term: \(6 \times 400 = 2400\).
This reduces computation time significantly during exams.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question is based on the topic of Ratio and Proportion.
We are given the ratio of four numbers as \(3:4:5:6\) and their combined sum as \(7200\).
We need to find the value of the largest number in this group.
The largest ratio term corresponds to the largest number.

Step 2: Key Formula or Approach:
Let the four numbers be represented as \(3x\), \(4x\), \(5x\), and \(6x\), where \(x\) is a common constant multiplier.
The sum of the four numbers can be mathematically expressed as:
\[ 3x + 4x + 5x + 6x = 7200 \]
After calculating the value of \(x\), the largest number is determined by evaluating \(6x\).

Step 3: Detailed Explanation:

• Let the four numbers be \(3x\), \(4x\), \(5x\), and \(6x\) respectively.

• According to the given condition, the sum of these four numbers is \(7200\).

• Therefore, we write the linear equation:
\[ 3x + 4x + 5x + 6x = 7200 \]

• Simplify the left-hand side of the equation by adding the coefficients of \(x\):
\[ 18x = 7200 \]

• Solve for \(x\) by dividing both sides of the equation by \(18\):
\[ x = \frac{7200}{18} \]
\[ x = 400 \]

• Now, we can calculate the individual values of each of the four numbers:
- The first number is \(3x = 3 \times 400 = 1200\).
- The second number is \(4x = 4 \times 400 = 1600\).
- The third number is \(5x = 5 \times 400 = 2000\).
- The fourth number (which has the largest ratio term) is \(6x = 6 \times 400 = 2400\).

• Comparing these values, the largest among the four numbers is indeed \(2400\).


Step 4: Final Answer:
The largest of the four numbers is \(2400\), which matches Option (D).