Sum of digit of two digit number is 11 . If the digit at tens place is increased by 5 and the digit at unit place is decreased by 5 the digits of the number are found to be reversed find the number
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X + Y = 11
10×(X+5) + (Y—5) = YX
10X + Y + 45 = YX
10X + Y — YX = —45
10X + Y —10Y — X = —45
9X — 9Y = —45
X — Y = — 5
X = Y—5
Y — 5 + Y = 11
2Y = 16
Y = 8
X = 8 — 5 = 3
10×(X+5) + (Y—5) = YX
10X + Y + 45 = YX
10X + Y — YX = —45
10X + Y —10Y — X = —45
9X — 9Y = —45
X — Y = — 5
X = Y—5
Y — 5 + Y = 11
2Y = 16
Y = 8
X = 8 — 5 = 3
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