The sum of digits of a two digit number is 9 the digit is reversed the new number decreased by 9 is equal to 4 times of orginal number find orginal number
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Step-by-step explanation:
Let the digit in the ten's place be x.
Let the digit in the unit place be y.
∴ The number will be = 10x+y
Also the sum of digits = 9
x+y = 9 (1)
On Reversing the order,the number we get will be
10y+x
Now From the question,
(10y+x−9) = 4(10x+y)
On simplification,
10y+x-9= 40x+4y
-9 = 40x + 4y - 10y - x
-9 = 39x - 6y
39x - 6y +9 = 0
We can take 3 as common in the above equation , so on dividing by 3,
13x - 2y + 3 = 0 (2)
From equation (1) we can derive the value of x ,
x = 9 - y (3)
On substituting value of x in (2) we get,
13 (9−y) −2y + 3 = 0
117 - 13y -2y +3 =0
117 - 15y + 3 = 0
120 - 15y = 0
120 = 15y
y = 120/15 = 8
On substituting value of y in (3),
x = 9 - 8
x = 1
∴ The required number = 18
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