Question

plz tell answer with explanation.​

Answer 1

Answer:

Solution:

Let the unit place digit of a two-digit number be x.

Therefore, the tens place digit = 9-x

∵ 2-digit number = 10 x tens place digit + unit place digit

∴ Original number = 10(9-x)+x

According to the question, New number

= Original number + 27

10x+left(9-x\right)=10\left(9-x\right)+x+27⇒10x+(9−x)=10(9−x)+x+27

10+9-x=90-10x+x+27⇒10+9−x=90−10x+x+27

9x+9=117-9x⇒9x+9=117−9x

9x+9x=117-9⇒9x+9x=117−9

18x=108⇒18x=108

x={108}{18}=6⇒x=18108

=6

Hence, the 2-digit number = 10(9-x)+x = 10(9-6)+6 = 10 x 3 + 6 = 30 + 6 = 36

$\huge\mathfrak\red{ur answer}$

Answer 2

Answer:

Question :-

• Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two digit number ?

Given :-

• Sum of the digits of a two digit number is 9.
• When we interchange the digits, it is found that the resulting new number is greater than the original number by 27.

To Find :-

• What is the two digit number.

Solution :-

Let,

$\mapsto \bf Ten's\: place =\: x$

$\mapsto \bf Unit's\: place =\: y$

Hence, the required numbers is :

$\leadsto \sf\bold{\green{Original\: Number =\: 10x + y}}$

Now,

$\bigstar$ Sum of the digits of a two digit number is 9.

$\implies \sf x + y =\: 9$

$\implies \sf\bold{\purple{x + y =\: 9\: ------\: (Equation\: No\: 1)}}$

$\bigstar$ When we interchange the digits we get :

$\leadsto \sf 10y + x$

$\bigstar$ When we interchange the digits, it is found that the resulting new number is greater than the original number 27.

$\implies \sf 10y + x =\: 27 + (10x + y)$

$\implies \sf 10y + x =\: 27 + 10x + y$

$\implies \sf 10y - y + x - 10x =\: 27$

$\implies \sf 9y - 9x =\: 27$

$\implies \sf 9(y - x) =\: 27$

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

$\implies \sf\bold{\purple{y - x =\: 3\: ------\: (Equation\: No\: 2)}}$

Now, by adding the equation no 1 with the equation no 2 we get,

$\implies \sf {\cancel{x}} + y + y {\cancel{- x}} =\: 9 + 3$

$\implies \sf y + y =\: 12$

$\implies \sf 2y =\: 12$

$\implies \sf y =\: \dfrac{\cancel{12}}{\cancel{2}}$

$\implies \sf\bold{\pink{y =\: 6}}$

By putting y = 6 in the equation no 1 we get,

$\implies \sf x + y =\: 9$

$\implies \sf x + 6 =\: 9$

$\implies \sf x =\: 9 - 6$

$\implies \sf\bold{\pink{x =\: 3}}$

Hence, the required original number will be :

$\longrightarrow \sf Original\: Number =\: 10x + y$

$\longrightarrow \sf Original\: Number =\: 10(3) + 6$

$\longrightarrow \sf Original\: Number =\: 30 + 6$

$\longrightarrow \sf\bold{\red{Original\: Number =\: 36}}$

${\small{\bold{\underline{\therefore\: The\: two\: digit\: number\: is\: 36\: .}}}}$