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If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is
- a)81
- b)72
- c)45
- d)54
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the sum of the digits of a two digit number is 9 and the difference...
From given question
x + y = 9 ...(i )
(10x + y) – (10y + x) = 45
9 (x – y) = 45
x – y = 5 ...(ii )
Solving equations (i ) and (ii ), we get
∴ x = 7, y = 2
So the number
= 10x + y
= 10 x 7 + 2
= 72
∴ 72 is the number
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Community Answer
If the sum of the digits of a two digit number is 9 and the difference...
To solve this problem, we need to find a two-digit number where the sum of its digits is 9 and the difference between the number and its reverse is 45.
Let's assume the two-digit number is represented as '10x + y', where x and y are the digits of the number.
Finding the sum of the digits:
The sum of the digits can be represented as x + y = 9.
Finding the difference between the number and its reverse:
The number can be represented as '10x + y', and its reverse can be represented as '10y + x'. The difference between the number and its reverse is (10x + y) - (10y + x) = 9x - 9y = 45.
From the equation x + y = 9, we can rearrange it to get y = 9 - x.
Substituting y = 9 - x in the equation 9x - 9y = 45, we get:
9x - 9(9 - x) = 45
Simplifying the equation,
9x - 81 + 9x = 45
18x - 81 = 45
18x = 45 + 81
18x = 126
x = 126/18
x = 7
Substituting the value of x in the equation y = 9 - x, we get:
y = 9 - 7
y = 2
Therefore, the two-digit number is 10x + y = 10(7) + 2 = 72.
Hence, the correct answer is option B, 72.
Let's assume the two-digit number is represented as '10x + y', where x and y are the digits of the number.
Finding the sum of the digits:
The sum of the digits can be represented as x + y = 9.
Finding the difference between the number and its reverse:
The number can be represented as '10x + y', and its reverse can be represented as '10y + x'. The difference between the number and its reverse is (10x + y) - (10y + x) = 9x - 9y = 45.
From the equation x + y = 9, we can rearrange it to get y = 9 - x.
Substituting y = 9 - x in the equation 9x - 9y = 45, we get:
9x - 9(9 - x) = 45
Simplifying the equation,
9x - 81 + 9x = 45
18x - 81 = 45
18x = 45 + 81
18x = 126
x = 126/18
x = 7
Substituting the value of x in the equation y = 9 - x, we get:
y = 9 - 7
y = 2
Therefore, the two-digit number is 10x + y = 10(7) + 2 = 72.
Hence, the correct answer is option B, 72.
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If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number isa)81b)72c)45d)54Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number isa)81b)72c)45d)54Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number isa)81b)72c)45d)54Correct answer is option 'B'. Can you explain this answer?.
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