Q24 of 186 Page 4

The sum of the digits of a two - digit number is 15. The number obtained by interchanging the digits exceeds the given number by 9. 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,


x + y = 15 …(i)


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


and 10x + y + 9 = x + 10y


⇒ 10x + y + 9 = x + 10y


⇒ 10x – x + y – 10y = – 9


⇒ 9x – 9y = – 9


⇒ x – y = – 1 …(ii)


On adding Eq. (i) and (ii) , we get


x + y + x – y = 15 – 1


⇒ 2x = 14


⇒ x = 7


On substituting the value of x = 5 in Eq. (i), we get


x + y = 15


⇒ 7 + y = 15


⇒ y = 8


So, the Original number = 10x + y


= 10×7 + 8


= 70 + 8


= 78


Hence, the two digit number is 78.


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