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Two numbers are such that the ratio between them is 3:4 but if each is increased by 3 then ratio becomes 4:5 find difference between the numbers?
  • a)
    3                             
  • b)
    9
  • c)
    2                             
  • d)
    7
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two numbers are such that the ratio between them is 3:4 but if each is...

15x + 15 = 16x + 12
3 = x 
Diff = 3
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Most Upvoted Answer
Two numbers are such that the ratio between them is 3:4 but if each is...
Understanding the Problem
We have two numbers, and their ratio is given as 3:4. This means we can express them in terms of a variable. Let:
- First number = 3x
- Second number = 4x
After increasing each number by 3, the new ratio becomes 4:5. We can set up the equation based on this new ratio:
- (3x + 3)/(4x + 3) = 4/5
Setting Up the Equation
Now, we will cross-multiply to eliminate the fraction:
- 5(3x + 3) = 4(4x + 3)
Expanding both sides gives us:
- 15x + 15 = 16x + 12
Solving for x
Next, we will rearrange the equation to isolate x:
- 15x + 15 - 12 = 16x
- 3 = 16x - 15x
- 3 = x
Now we substitute the value of x back to find the actual numbers:
- First number = 3x = 3(3) = 9
- Second number = 4x = 4(3) = 12
Finding the Difference
To find the difference between the two numbers:
- Difference = 12 - 9 = 3
Conclusion
Thus, the difference between the two numbers is 3. Therefore, the correct answer is option 'A'.
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