Mathematics
The sum of the digits of a two digit number is 5. If the digits are reversed, the number is reduced by 27. Find the number.
Linear Equations
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Answer
Let digit at unit's place be x and ten's place be y.
Number = 10 × y + x = 10y + x
Given,
Sum of the digits of a two digit number is 5.
∴ x + y = 5
⇒ x = 5 - y ……..(1)
If the digits are reversed, then number = 10x + y.
Given,
If the digits are reversed, the number is reduced by 27.
∴ 10x + y = 10y + x - 27
⇒ 10x - x = 10y - y - 27
⇒ 9x = 9y - 27
⇒ 9x = 9(y - 3)
⇒ x = y - 3 ……..(2)
From (1) and (2), we get :
⇒ y - 3 = 5 - y
⇒ y + y = 5 + 3
⇒ 2y = 8
⇒ y = = 4.
Substituting value of y in equation (2), we get :
⇒ x = 4 - 3 = 1.
Number = 10y + x = 10(4) + 1 = 40 + 1 = 41.
Hence, the number = 41.
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