Question 858689
10. Let the unit's digit and ten's digit of the two digit number be X and Y respectively.


The number in the unit’s place is 4 more than the number in the ten’s place.
X = Y + 4 __________ (1)


If the digits of the number are reversed, the new number is 6 more than thrice the original number.
10X + Y = 3(10Y + X) + 6
10X + Y = 30Y + 3X + 6
7X - 29Y = 6 ____________ (2)


Substituting X = Y + 4 from equation (1) into (2)
7(Y + 4) - 29Y = 6
7Y + 28 - 29Y = 6
22Y = 22
Y = 1
X = Y + 4 = 5


So the two digit number is 15.

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