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The difference between two numbers is 5. If 25 is subtracted from the smaller number and 20 is added to the greater number the ratio becomes 1 : 2. What is the greater number?
  • a)
    80
  • b)
    90
  • c)
    85
  • d)
    75
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The difference between two numbers is 5. If 25 is subtracted from the ...
Given:
Difference between the two numbers = 5
Ratio If 25 is subtracted from the smaller number and 20 is added to the greater number = 1 : 2
Calculation:
Let the greater number and smaller number be x and (x – 5) respectively
Now, according to the question,
(x – 5 – 25) : (x + 20) = 1 : 2
⇒ (x –  30)/(x + 20) = 1/2
⇒ 2x – 60= x + 20
⇒ x = 80
∴ The greater number is 80
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Most Upvoted Answer
The difference between two numbers is 5. If 25 is subtracted from the ...
Given:
Difference between the two numbers = 5
Ratio If 25 is subtracted from the smaller number and 20 is added to the greater number = 1 : 2
Calculation:
Let the greater number and smaller number be x and (x – 5) respectively
Now, according to the question,
(x – 5 – 25) : (x + 20) = 1 : 2
⇒ (x –  30)/(x + 20) = 1/2
⇒ 2x – 60= x + 20
⇒ x = 80
∴ The greater number is 80
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Community Answer
The difference between two numbers is 5. If 25 is subtracted from the ...
Understanding the Problem
We have two numbers, which we can denote as x (greater number) and y (smaller number).
Key Conditions
- The difference between the two numbers is 5:
- x - y = 5
- If 25 is subtracted from the smaller number and 20 is added to the greater number, the ratio of the two becomes 1:2:
- (y - 25) / (x + 20) = 1 / 2
Setting Up Equations
1. From the first condition:
- x = y + 5
2. Substituting x in the second condition:
- (y - 25) / ((y + 5) + 20) = 1 / 2
- This simplifies to (y - 25) / (y + 25) = 1 / 2
Cross-Multiplying
Cross-multiplying gives us:
- 2(y - 25) = 1(y + 25)
This expands to:
- 2y - 50 = y + 25
Solving for y
Rearranging the equation:
- 2y - y = 25 + 50
- y = 75
Finding the Greater Number
Using the relationship x = y + 5:
- x = 75 + 5
- x = 80
Conclusion
The greater number is 80.
Thus, the correct answer is option 'A'.
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The difference between two numbers is 5. If 25 is subtracted from the smaller number and 20 is added to the greater number the ratio becomes 1 : 2. What is the greater number?a)80b)90c)85d)75Correct answer is option 'A'. Can you explain this answer?
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