Question

two digit number is 4 times the sum of its digits.if 18 is added in this number then the place of digits are changed. the number is?

Answer 1

Let the digit in one's place be x and the digit in ten's place be y.

Therefore, the required decimal expansion is 10y + x ---------- (*)

Given that two digit number is 4 times the sum of its digits.

= > 10y + x = 4(x + y)

= > 10y + x = 4x + 4y

= > 3x - 6y = 0

= > 3(x - 2y) = 0

= > x - 2y = 0

= > x = 2y ---- (1)

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Given that is 18 is added in this number then the place of digits are changed.

= > 10y + x + 18 = 10x + y

= > 10y + 2y + 18 = 10(2y) + y

= > 12y + 18 = 20y + y

= > 12y + 18 = 21y

= > 18 = 9y

= > y = 2.

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Substitute y = 2 in (1),we get

= > x = 2y

= > x = 4.

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Substitute x,y in (*), we get

= > 10y + x

= > 10(2) + 4)

= > 24.

Therefore, the number is 24.

Hope this helps!