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 ( )

  1. Caroline
    0
    2021-08-20T19:18:32+00:00
    Reply

    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....❶

    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....❷

    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 ❞

    ______________________

  2. Faith
    0
    2021-08-20T19:18:56+00:00
    Reply

    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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