Q9 of 37 Page 35

A number consists of two digits whose sum is 9. If 9 is subtracted from the no. the digit interchange their places. Find the number.

Let x and y are the two digits of a two - digit number.

Therefore, the two - digit number = 10x + y and the reversed number = 10y + x


According to the question


⇒ x + y = 9 ……(i)


Also,


⇒ 10x + y – 9 = 10y + x


⇒ 9x – 9y = 9


⇒ x – y = 1 ……(ii)


Adding equation (i) and equation (ii)


⇒ 2x = 10


⇒ x = 5


Hence, y = 9 – x = 9 – 5 = 4


Therefore, the two digit number = 10x + y = (10 × 5) + 4 = 54


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