The product of a two-digit number is 8. When 18 is added to the number the digits were reversed. What was the number? Ticka 18 tickb 24 tickc 42 tickd 81
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X × Y = 8
(X × 10) + Y + 18 = (Y × 10) + X
10X + Y + 18 = 10Y + X
9X - 9Y = -18
X - Y = -2
X = Y - 2. ---------> (1)
X × Y = 8
from (1)
(Y - 2 ) × Y = 8
Y^2 - 2Y = 8
Y^2 - 2Y - 8 = 0
=> Y = 4
=> X = 2
(X × 10) + Y + 18 = (Y × 10) + X
10X + Y + 18 = 10Y + X
9X - 9Y = -18
X - Y = -2
X = Y - 2. ---------> (1)
X × Y = 8
from (1)
(Y - 2 ) × Y = 8
Y^2 - 2Y = 8
Y^2 - 2Y - 8 = 0
=> Y = 4
=> X = 2
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