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A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.
- a)54
- b)53
- c)45
- d)55
Correct answer is option 'C'. Can you explain this answer?
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A number between 10 and 100 is five times the sum of its digits. If 9 ...
Given information:
- A number between 10 and 100 is five times the sum of its digits.
- If 9 is added to it, the digits are reversed.
To find: The number
Solution:
Let the number be represented by 'xy', where x and y are the digits.
According to the first condition, we can write:
10 < xy="" />< />
xy = 5(x + y)
Simplifying the second equation, we get:
xy = 5x + 5y
xy - 5x - 5y = 0
x(y - 5) - 5y = 0
x(y - 5) = 5y
Since x and y are digits, y cannot be zero. Hence, we can divide both sides by y:
x(y - 5) / y = 5
Expanding the left side:
x - (5x / y) = 5
Since x and y are digits, 5x / y can only be 0, 5, 10, 15, or 20.
- If 5x / y = 0, then x = 5, which is not possible since x is a digit between 1 and 9.
- If 5x / y = 5, then x = y, which gives the number 11. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 10, then x = 2y, which gives the number 25. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 15, then x = 3y, which gives the number 35. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 20, then x = 4y, which gives the number 45. This number satisfies both conditions.
Now, we need to check if adding 9 to 45 gives us the reversed digits.
45 + 9 = 54
Therefore, the answer is option C, 45.
- A number between 10 and 100 is five times the sum of its digits.
- If 9 is added to it, the digits are reversed.
To find: The number
Solution:
Let the number be represented by 'xy', where x and y are the digits.
According to the first condition, we can write:
10 < xy="" />< />
xy = 5(x + y)
Simplifying the second equation, we get:
xy = 5x + 5y
xy - 5x - 5y = 0
x(y - 5) - 5y = 0
x(y - 5) = 5y
Since x and y are digits, y cannot be zero. Hence, we can divide both sides by y:
x(y - 5) / y = 5
Expanding the left side:
x - (5x / y) = 5
Since x and y are digits, 5x / y can only be 0, 5, 10, 15, or 20.
- If 5x / y = 0, then x = 5, which is not possible since x is a digit between 1 and 9.
- If 5x / y = 5, then x = y, which gives the number 11. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 10, then x = 2y, which gives the number 25. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 15, then x = 3y, which gives the number 35. However, this number does not satisfy the condition that it is between 10 and 100.
- If 5x / y = 20, then x = 4y, which gives the number 45. This number satisfies both conditions.
Now, we need to check if adding 9 to 45 gives us the reversed digits.
45 + 9 = 54
Therefore, the answer is option C, 45.
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A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.a)54b)53c)45d)55Correct answer is option 'C'. Can you explain this answer?
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A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.a)54b)53c)45d)55Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.a)54b)53c)45d)55Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.a)54b)53c)45d)55Correct answer is option 'C'. Can you explain this answer?.
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