If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then

Question

If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is A.81 B.72 C.45 D.54

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Faith 3 weeks 2021-08-20T19:17:17+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-20T19:18:32+00:00

    GIVEN:

    • Sum of the digits of a two digit number is 9
    • Difference between the number and that formed by reversing the digits is 45

    TO FIND:

    • What is the original number ?

    SOLUTION:

    Let the digit at unit’s place be ‘y’ and the digit at ten’s place be ‘x’

    CASE: 1)

    Sum of the digits of a two digit number is 9.

    According to question:

    x + y = 9

    x = 9 y....

    CASE:- 2)

    Difference between the number and that formed by reversing the digits is 45.

    Reversed Number = 10y + x

    Original Number Reversed Number = 45

    According to question:

    10x + y –(10y + x) = 45

    10x + y –10y –x = 45

    9x –9y = 45

    Taking common 9 from both sides

    x y = 5....

    Put the value of ‘x’ in equation 2)

    9 –y –y = 5

    9 –2y = 5

    –2y = 5 –9

    –2y = –4

    y = \sf{\cancel\dfrac{-4}{-2}}

    y = 2

    Put the value of ‘y’ in equation 1)

    x = 9 –2

    x = 7

    NUMBER = 10x + y

    NUMBER = 10(7) + 2

    NUMBER = 70 + 2

    NUMBER = 72

    Hence, the number formed is 72

    ______________________

    0
    2021-08-20T19:18:56+00:00

    Question:

    If the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 45 then number is

    A) 81

    B) 72

    C) 45

    D) 54

    Answer:

    Original number:

    Let the digit in unit’s place be x

    Then the digit in ten’s place will be (9 – x) [As the sum of digit is 9]

    Hence, the number is 10(9 – x) + x = 90 – 9x

    New reversed number:-

    Digit in unit’s place will be (9 – x)

    Digit in ten’s place will be x

    Hence, the number is 10x + (9 – x) = 9x + 9

    We know that,

    Original number – new number = 45

    => 90 – 9x – (9x + 9) = 45

    => 90 – 9x – 9x – 9 = 45

    => -18x = -36

    => x = 2

    Hence,

    original number = 90 – 9x = 90 – 18 = 72

    Ans. Original number = B) 72

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