A two digit no.is 4 times the sum of its digit .If 18 is added to the no,the digits are reversed.Find the no.
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a two digit number is 4 times the sum of it's digit so,
10x + y = 4(x +y)
if 18 is added to the number, digits get reversed so,
18 + 10x + y = 10y + x
18 + 10x - x = 10y - y
18 + 9x = 9y
divide by 9 on both sides
2 + x = y (substitute y in first equation)
10x + (x + 2) = 4(x + (x + 2))
10x + x + 2 = 4x + 4(x + 2)
11x + 2 = 4x + 4x + 8
11x - 8x = 8 - 2
3x = 6
x = 2
y = x + 2 = 2 + 2 = 4
so the two digit number is 10x + y = 10*2 + 4 = 24
10x + y = 4(x +y)
if 18 is added to the number, digits get reversed so,
18 + 10x + y = 10y + x
18 + 10x - x = 10y - y
18 + 9x = 9y
divide by 9 on both sides
2 + x = y (substitute y in first equation)
10x + (x + 2) = 4(x + (x + 2))
10x + x + 2 = 4x + 4(x + 2)
11x + 2 = 4x + 4x + 8
11x - 8x = 8 - 2
3x = 6
x = 2
y = x + 2 = 2 + 2 = 4
so the two digit number is 10x + y = 10*2 + 4 = 24
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