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The sum of three numbers is 123. If the ratio between first and second numbers is 2:5 and that of between second and third is 3:4, then find the difference between second and the third number.
  • a)
    12
  • b)
    14
  • c)
    15
  • d)
    17
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The sum of three numbers is 123. If the ratio between first and second...
Answer – C.15 Explanation : a:b = 2:5 and b:c = 3:4 so a:b:c = 6:15:20 41x = 123, X = 3. And 5x = 15
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Most Upvoted Answer
The sum of three numbers is 123. If the ratio between first and second...
Given:
- Sum of three numbers = 123
- Ratio between first and second numbers = 2:5
- Ratio between second and third numbers = 3:4

To find:
Difference between the second and third numbers

Solution:
Let's assume the three numbers as follows:
First number = 2x
Second number = 5x
Third number = 4y

Step 1: Finding the value of x
According to the given information, the sum of the three numbers is 123:
2x + 5x + 4y = 123

Simplifying the equation:
7x + 4y = 123 --(1)

Step 2: Finding the value of y
The ratio between the second and third numbers is given as 3:4:
5x / 4y = 3 / 4

Cross-multiplying the ratio:
5x * 4 = 3 * 4y

Simplifying the equation:
20x = 12y --(2)

Step 3: Solving the equations
We have two equations:
7x + 4y = 123 --(1)
20x = 12y --(2)

Multiplying equation (1) by 3 and equation (2) by 7 to eliminate y:
21x + 12y = 369 --(3)
140x = 84y --(4)

Substituting the value of 12y from equation (2) into equation (4):
140x = 84 * 20x

Simplifying the equation:
140x = 1680x

Dividing both sides by x:
140 = 1680

This is not possible, which means there is no solution for this system of equations. Therefore, the given ratios are not consistent with the sum of three numbers being 123.

Hence, the correct answer is e) None of these
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The sum of three numbers is 123. If the ratio between first and second numbers is 2:5 and that of between second and third is 3:4, then find the difference between second and the third number.a)12b)14c)15d)17e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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