Q19 of 186 Page 4

A two - digit number is 4 times the sum of its digits. If 18 is added to 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 two digit number = 10x + y


The sum of the digit = x + y


According to the question,


(10x + y) = 4(x + y)


⇒ 10x + y = 4x + 4y


⇒ 10x – 4x + y – 4y = 0


⇒ 6x – 3y = 0


⇒ 2x – y = 0


⇒ y = 2x …(i)


After interchanging the digits, New number = x + 10y


and 10x + y + 18 = x + 10y


⇒ 10x + y + 18 = x + 10y


⇒ 10x – x + y – 10y = – 18


⇒ 9x – 9y = – 18


⇒ x – y = – 2 …(ii)


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


x – y = – 18


⇒ x – 2x = – 2


⇒ – x = – 2


⇒ x = 2


On putting the value of x = 2 in Eq. (i), we get


y = 2×2 = 4


So, the Original number = 10x + y


= 10×2 + 4


= 20 + 4


= 24


Hence, the two digit number is 24.


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