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The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is
- a)5
- b)4
- c)3
- d)2
Correct answer is option 'C'. Can you explain this answer?
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The ratio of a two-digit natural number to a number formed by reversin...
Explanation:
Let the two-digit number be "10x + y".
When the digits are reversed, the number becomes "10y + x".
Given, (10x + y)/(10y + x) = 4/7
Cross-multiplying, we get 70x + 7y = 40y + 4x
Simplifying, we get 66x = 33y
Therefore, x = y * 2
Since x and y are digits, the only possible values for y are 1, 2, 3, 4, and 5.
If y = 1, then x = 2, which gives the number 12.
If y = 2, then x = 4, which gives the number 24.
If y = 3, then x = 6, which gives the number 36.
If y = 4, then x = 8, which gives the number 48.
If y = 5, then x = 10, which gives the number 50.
Therefore, there are only 3 pairs of two-digit numbers that satisfy the given condition.
Hence, option C is the correct answer.
Let the two-digit number be "10x + y".
When the digits are reversed, the number becomes "10y + x".
Given, (10x + y)/(10y + x) = 4/7
Cross-multiplying, we get 70x + 7y = 40y + 4x
Simplifying, we get 66x = 33y
Therefore, x = y * 2
Since x and y are digits, the only possible values for y are 1, 2, 3, 4, and 5.
If y = 1, then x = 2, which gives the number 12.
If y = 2, then x = 4, which gives the number 24.
If y = 3, then x = 6, which gives the number 36.
If y = 4, then x = 8, which gives the number 48.
If y = 5, then x = 10, which gives the number 50.
Therefore, there are only 3 pairs of two-digit numbers that satisfy the given condition.
Hence, option C is the correct answer.
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The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs isa)5b)4c)3d)2Correct 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 The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs isa)5b)4c)3d)2Correct 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 The ratio of a two-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs isa)5b)4c)3d)2Correct answer is option 'C'. Can you explain this answer?.
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