Q23 of 186 Page 4

A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

Let unit’s digit = y

and the ten’s digit = x


So, the original number = 10x + y


The sum of the number = 10x + y


The sum of the digit = x + y


According to the question,


10x + y = 7(x + y)


⇒ 10x + y = 7x + 7y


⇒ 10x + y – 7x – 7y = 0


⇒ 3x – 6y = 0


⇒ x – 2y = 0


⇒ x = 2y …(i)


The reverse number = x + 10y


and 10x + y – 27 = x + 10y


⇒ 10x + y – 27 = x + 10y


⇒ 10x – x + y – 10y = 27


⇒ 9x – 9y = 27


⇒ x – y = 3 …(ii)


On substituting the value of x = 2y in Eq. (ii), we get


x – y = 3


⇒ 2y – y = 3


⇒ y = 3


On putting the value of y = 3 in Eq. (i), we get


x = 2(3) = 6


So, the Original number = 10x + y


= 10×6 + 3


= 60 + 3


= 63


Hence, the two digit number is 63.


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