Question
When the digits of a two-digit number are interchanged,
the new number becomes 19 less than 150% of the original number. If the sum of the digits is 11, find the original number.Solution
Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
Original number = (10x + y)
According to the data given:Â
10y + x = 1.5 × (10x + y) − 19
Multiplying both sides by 2,Â
20y + 2x = 30x + 3y − 38Â
⇒ 28x − 17y = 38 …. (I)
And, x + y = 11 …. (II)
From (II), x = 11 − y. Substitute in (I):Â
28(11 − y) − 17y = 38Â
308 − 45y = 38Â
45y = 270Â
y = 6
Then x = 5.Â
So, original number = 10 × 5 + 6 = 56.
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