Q99 of 113 Page 110

In a two-digit number, digit in unit’s place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number.

Let us assume, is the tenth-place digit and is the unit

Place digit of a two – digit number


The two digit number = 10x + y and reversed number = 10y + x


According to the question


y = 2x⋯(i)


Given,


10x + y + 27 = 10y + x


9y-9x = 27


y-x = 3


(divide by 9 on both the sides)


y = 3 + x⋯(ii)


Substitute the value of y from (i) in(ii)


2x = 3 + x


2x-x = 3


x = 3


∴y = 2x = 2 × 3 = 6


Hence the two digit number = 10x + y = 10 × 3 + 6 = 36


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