Mathematics
The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is 32. Find the number.
Answer
Let ten's digit be x and unit's digit be y.
Given,
The ten's digit of a two digit number is three times the unit digit.
∴ x = 3y ………..(1)
Given,
The sum of the number and the unit digit is 32.
Number = 10x + y, unit's digit = y
∴ 10x + y + y = 32
⇒ 10x + 2y = 32
⇒ 2(5x + y) = 32
⇒ 5x + y = 16
⇒ 5(3y) + y = 16 ……..[From (1)]
⇒ 15y + y = 16
⇒ 16y = 16
⇒ y = 1.
⇒ x = 3y = 3(1) = 3.
Number = 10x + y = 10(3) + 1 = 31.
Hence, number = 31.
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