Question

2. The sum of the digits of a two digit number is 7
If the digits are reversed, the number is reduced
by 27. Find the number,​

Answer 1

AnswEr :

25.

$\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$

The sum of the digits of a two digit number is 7. If the digits are reversed, the number is reduced by 27.

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

The number.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

Let the ten's place be R

Let the one's place be M

$\bf{\large{\underline{\sf{\dag{The\:original\:number=10R+M.}}}}}}\\\\\ \bf{\large{\underline{\sf{\dag{The\:reversed\:number=10M+R.}}}}}}}$

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\dashrightarrow\tt{R+M=7}\\\\\\\dashrightarrow\tt{\red{R=7-M................................(1)}}$

&

$\mapsto\tt{10R+M=10M+R-27}\\\\\\\mapsto\tt{10R-R+M-10M=-27}\\\\\\\mapsto\tt{9R-9M=-27}\\\\\\\mapsto\tt{9(R-M)=-27}\\\\\\\mapsto\tt{R-M=\cancel{\dfrac{-27}{9}}} \\\\\\\mapsto\tt{R-M=-3}\\\\\\\mapsto\tt{7-M-M=-3\:\:\:\:\:\:\:\:\:\:\:\big[from(1)\big]}\\\\\\\mapsto\tt{7-2M=-3}\\\\\\\mapsto\tt{-2M=-3-7}\\\\\\\mapsto\tt{-2M=-10}\\\\\\\mapsto\tt{M=\cancel{\dfrac{-10}{-2} }}\\\\\\\mapsto\tt{\green{M=5}}$

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

$\dashrightarrow\tt{R=7-5}\\\\\\\dashrightarrow\tt{\green{R=2}}$

$\bf{\orange{\underline{\underline{\bf{\blacksquare{The\:Number\:required\::}}}}}}$

$\hookrightarrow\tt{10R+M}\\\\\\\hookrightarrow\tt{10(2)+5}\\\\\\\hookrightarrow\tt{20+5}\\\\\\\hookrightarrow\tt{\purple{25}}$

Answer 2

Answer:

25

Step-by-step explanation:

Given:

Sum of digits of two digit number is 7,

After reversing digits the number is reduced by 27

To Find:

Solution: 

1)Let the tens digit no. be X

2)Let unit digit of the number be y

→ x + y = 7......(1)

According to question,

→ The two digit number is 10x + y and after reversing it's digit the number becomes 10y +x

Therefore equation becomes,

⟹ 10y + x = 10x + y + 27

⟹ 10y – y = 10x – x + 27⟹ 9y = 9x + 27

⟹ 9y – 9x = 27

⟹ 9 ( y – x) = 27

⟹ y – x = 27/9 = 3

⟹ y = 3 + x

Putting y = 3 + x in equation 1

⟹ x + 3+ x = 7

⟹ 2x = 7 – 3

⟹ 2x = 4

⟹ x = 2

Therefore "y" will be,

⟹ y = 2 + 3 = 5

Hence, The two digit number is 25