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The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.
- a)57
- b)75
- c)85
- d)58
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sum of the digits of a two-digit number is 12. The number obtained...
Let the unit’s and ten’s digits in the number be y and x respectively.
So, the number be 10x + y.
According to the question, x + y = 12
Also, 10x + y + 18 = 10y + x
⇒ 9x – 9y = –18 ⇒ x – y = –2
Solving (1) and (2), we get x = 5 and y = 7
∴ Required number is 57.
So, the number be 10x + y.
According to the question, x + y = 12
Also, 10x + y + 18 = 10y + x
⇒ 9x – 9y = –18 ⇒ x – y = –2
Solving (1) and (2), we get x = 5 and y = 7
∴ Required number is 57.
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Community Answer
The sum of the digits of a two-digit number is 12. The number obtained...
Understanding the problem:
The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18.
Let's solve the problem step by step:
- Let the tens digit be x and the units digit be y.
- According to the given condition, x + y = 12 ...(1)
- The number formed by the digits is 10x + y.
- The number obtained by interchanging the digits is 10y + x.
- According to the second condition, 10y + x = 10x + y + 18
- Simplifying the equation, we get 9y - 9x = 18
- Dividing by 9, we get y - x = 2 ...(2)
Solving equations (1) and (2):
- Adding equations (1) and (2), we get 2y = 14
- Solving for y, we get y = 7
- Substituting y = 7 in equation (1), we get x = 5
Therefore, the two-digit number is 57.
- The number obtained by interchanging the digits is 75.
- 75 exceeds 57 by 18, which satisfies the given condition.
Hence, the correct answer is option 'A' (57).
The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18.
Let's solve the problem step by step:
- Let the tens digit be x and the units digit be y.
- According to the given condition, x + y = 12 ...(1)
- The number formed by the digits is 10x + y.
- The number obtained by interchanging the digits is 10y + x.
- According to the second condition, 10y + x = 10x + y + 18
- Simplifying the equation, we get 9y - 9x = 18
- Dividing by 9, we get y - x = 2 ...(2)
Solving equations (1) and (2):
- Adding equations (1) and (2), we get 2y = 14
- Solving for y, we get y = 7
- Substituting y = 7 in equation (1), we get x = 5
Therefore, the two-digit number is 57.
- The number obtained by interchanging the digits is 75.
- 75 exceeds 57 by 18, which satisfies the given condition.
Hence, the correct answer is option 'A' (57).
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