Practice Test Discussion

Q)

If the number obtained on the interchanging the digits of two digit number is 18 more than the original number and the sum of the digits is 8, then what is the original number?

    • Explanation

    Let the ten's digit be 'x' and unit's digit be 'y'

    Then, two digit number =10x+y

    According to the question

    ⇒ x+y=8  ---Eq(1)

    Again,

    ⇒ 10x+y=18(10y+x)

    ⇒ 10x+y-10y-x=18

    ⇒ 10x-x+y-10y=18

    ⇒ 9x-9y=18

    ⇒ x-y=2   ---Eq(2)

    Substitute Eq(1) from Eq(2) we get 

    ⇒ -2y=-6

    ⇒ y=3

    Substitute 'y' value in Eq(1)

    ⇒ x+3=8

    ⇒ x=5

    ∴ The number is ⇒ 10x+y

    ⇒ 10×5+3

    ⇒ 53.

    Hence, Option D is correct.

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