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The sum of four numbers is 255. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?
  • a)
    72
  • b)
    132
  • c)
    60
  • d)
    66
Correct answer is option 'D'. Can you explain this answer?
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The sum of four numbers is 255. The ratio of the first number to the s...
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The sum of four numbers is 255. The ratio of the first number to the s...
Given information:
- The sum of four numbers is 255.
- The ratio of the first number to the second number is 2:3.
- The ratio of the second number to the third number is 5:6.
- The ratio of the third number to the fourth number is 8:9.

Let's solve this step by step:

Step 1: Express the ratios in terms of a common variable.
- Let the first number be 2x.
- Let the second number be 3x.
- Let the third number be 5y.
- Let the fourth number be 6y.

Step 2: Set up an equation using the sum of the four numbers.
2x + 3x + 5y + 6y = 255

Step 3: Simplify the equation.
5x + 11y = 255

Step 4: Solve for one variable in terms of the other.
5x = 255 - 11y
x = (255 - 11y) / 5

Step 5: Substitute the value of x in terms of y into the ratios.
- The first number = 2x = 2 * [(255 - 11y) / 5] = (510 - 22y) / 5
- The second number = 3x = 3 * [(255 - 11y) / 5] = (765 - 33y) / 5
- The third number = 5y
- The fourth number = 6y

Step 6: Set up an equation using the ratios.
[(510 - 22y) / 5] + [(765 - 33y) / 5] + 5y + 6y = 255

Step 7: Simplify the equation.
(510 - 22y + 765 - 33y + 25y + 30y) / 5 = 255

Step 8: Combine like terms.
(510 + 765 + 25y) / 5 = 255

Step 9: Simplify further.
(1275 + 25y) / 5 = 255

Step 10: Multiply both sides of the equation by 5.
1275 + 25y = 255 * 5

Step 11: Simplify further.
1275 + 25y = 1275

Step 12: Subtract 1275 from both sides of the equation.
25y = 0

Step 13: Divide both sides of the equation by 25.
y = 0

Step 14: Substitute the value of y into the ratios to find the other variables.
- The first number = (510 - 22y) / 5 = (510 - 0) / 5 = 102
- The second number = (765 - 33y) / 5 = (765 - 0) / 5 = 153
- The third number = 5y = 5 * 0 = 0
- The fourth number = 6y = 6 * 0 = 0

Step 15: Find the average of the second number and the third number.
Average = (Second number + Third number) / 2 = (153 + 0) / 2 = 153 / 2 = 76.
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The sum of four numbers is 255. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer?
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The sum of four numbers is 255. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of four numbers is 255. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of four numbers is 255. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer?.
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