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Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?
- a)6
- b)12
- c)15
- d)21
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two numbers are in the ratio 2:5. If 6 is added to both, their ratio c...
(2A + 6)/(5A + 6) = 4/7
14A + 42 = 20A + 24, A = 3
Larger number = 5A = 15
14A + 42 = 20A + 24, A = 3
Larger number = 5A = 15
Most Upvoted Answer
Two numbers are in the ratio 2:5. If 6 is added to both, their ratio c...
Understanding the Problem
We have two numbers in the ratio 2:5. Let's denote these numbers as:
- First Number = 2x
- Second Number = 5x
After adding 6 to both numbers, their ratio changes to 4:7.
Setting Up the Equation
When we add 6 to both numbers, we can express the new situation as:
- New First Number = 2x + 6
- New Second Number = 5x + 6
According to the problem, the new ratio is:
(2x + 6) / (5x + 6) = 4/7
Cross-Multiplying to Solve
To eliminate the fraction, we can cross-multiply:
7(2x + 6) = 4(5x + 6)
This simplifies to:
14x + 42 = 20x + 24
Rearranging the Equation
Next, we rearrange it to isolate x:
14x - 20x = 24 - 42
This gives us:
-6x = -18
Thus, we find:
x = 3
Finding the Numbers
Now that we have x, we can find the original numbers:
- First Number = 2x = 2(3) = 6
- Second Number = 5x = 5(3) = 15
Conclusion
The larger number is:
- 15
Thus, the correct answer is option 'C'.
We have two numbers in the ratio 2:5. Let's denote these numbers as:
- First Number = 2x
- Second Number = 5x
After adding 6 to both numbers, their ratio changes to 4:7.
Setting Up the Equation
When we add 6 to both numbers, we can express the new situation as:
- New First Number = 2x + 6
- New Second Number = 5x + 6
According to the problem, the new ratio is:
(2x + 6) / (5x + 6) = 4/7
Cross-Multiplying to Solve
To eliminate the fraction, we can cross-multiply:
7(2x + 6) = 4(5x + 6)
This simplifies to:
14x + 42 = 20x + 24
Rearranging the Equation
Next, we rearrange it to isolate x:
14x - 20x = 24 - 42
This gives us:
-6x = -18
Thus, we find:
x = 3
Finding the Numbers
Now that we have x, we can find the original numbers:
- First Number = 2x = 2(3) = 6
- Second Number = 5x = 5(3) = 15
Conclusion
The larger number is:
- 15
Thus, the correct answer is option 'C'.
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Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer?
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Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer?.
Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two numbers are in the ratio 2:5. If 6 is added to both, their ratio changes to 4:7. What is the larger number?a)6b)12c)15d)21Correct answer is option 'C'. Can you explain this answer?.
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