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A number consisting of two digits is four times the sum of its digits and if 27 be added to it the digits are reversed. The number is :
  • a)
    63
  • b)
    35
  • c)
    36
  • d)
    60
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A number consisting of two digits is four times the sum of its digits ...
Given information:
- A two-digit number
- Four times the sum of its digits
- If 27 is added to it, the digits are reversed

Let's assume the number to be xy, where x and y are the digits of the number.

Four times the sum of its digits:
- 4(x+y)

Adding 27 to the number:
- xy + 27

The digits are reversed:
- 10y + x

Equating the two expressions for the same number:
- 4(x+y) = 10y + x - 27

Simplifying the equation:
- 3x - 6y = -27
- x - 2y = -9

As x and y are digits, x can be 1, 2, 3, 4, 5, 6, 7, 8 or 9 and y can be 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.

Checking each value of x and y, we get:
- x = 3 and y = 6
- 4(x+y) = 36 and xy = 36 - 27 = 9
- The number is 36

Therefore, the answer is option C) 36.
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A number consisting of two digits is four times the sum of its digits ...
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A number consisting of two digits is four times the sum of its digits and if 27 be added to it the digits are reversed. The number is :a)63b)35c)36d)60Correct answer is option 'C'. Can you explain this answer?
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