Question

The difference of digits of a two digit number is 3 . on reversing the order of digits ,the new number is diminshed by 27 than original number. find the number ​

Answer 1

$\bf{\Huge{\underline{\boxed{\bf{\orange{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\sf{\green{Given\::}}}}}$

The difference of digit of a two digit number is 3, on reversing the order of digits, the new number is diminished by 27 than original number.

$\bf{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The number.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

Let the two digit number be RM

• The original number = 10R + M
• The reversed number = 10M + R

A/q

→ R - M = 3.............................(1)

&

Reversing the order digit, the new number is diminished by 27, we get;

→ 10M + R = 10R + M - 27

→ 10M - M + R - 10R = -27

→ 9M - 9R = -27

→ 9(M - R) = -27

→ M - R = $\bf{\cancel{\frac{-27}{9} }}$

→ M - R = -3

→ M = -3 + R..............................(2)

Putting the value of M in equation (1), we get;

→ R - (-3) + R = 3

→ R + 3 + R = 3

→ 2R = 3 - 3

→ 2R = 0

→ R = 0/2

→ R = 0

Putting the value of R in equation (2), we get;

→ M = -3 + 0

→ M = -3

Thus,

The original number is 10(0) + (-3) = 0 - 3 = -3

Answer 2

$\large{\underline{\underline{\mathfrak{\red{\sf{Answer-}}}}}}$

Number = 85

$\large{\underline{\underline{\mathfrak{\red{\sf{Explanation-}}}}}}$

$\bold{\underline{\green{\sf{Given-}}}}$

• The difference of digits of a two digit number is 3.

• On reversing the order of digits, the new number is diminshed by 27 than original number.

$\bold{\underline{\green{\sf{To\:find-}}}}$

• The number.

$\bold{\underline{\green{\sf{Solution-}}}}$

Let the unit digit be x and tens digit be y. [ say x > y ]

Number = 10x + y

Case 1) : The difference of digits of a two digit number is 3.

$\blue{\sf{x-y=3}}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (1)

Case 2) : On reversing the order of digits, the new number is diminshed by 27 than original number.

On reversing the digit, number = 10y + x

$\implies$ $\sf{10y+x=(10x+y)-27}$

$\implies$ $\sf{10y-y+x-10x=-27}$

$\implies$ $\sf{9y-9x=-27}$

$\implies$ $\sf{\cancel9(y-x=-3)}$

$\implies$ $\blue{\sf{y-x=-3}}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀–eq (2)

It is not possible to solve equation (1) and (2) as both x and y are cancelled to each other.

So here, y must be more than x, let we choose y be 8 and x be 5. [ 8 - 5 = 3 ]

Number = 85

★Note : You can choose any number whose difference is 3.

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#Answerwithquality

#BAL! :)

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