Question

the sum of the digit of a two digit is 7 . the number formed by reversing the digit is 45 more than the original number . find the original number

Answer 1

$\huge\bf\green{Hey \: there!}$


▶ Given


i) The sum of the digits of a two digit number is 7


ii) The number formed by reversing the digit is 45 more than the original number


▶ Let :


i) Let the two digit number be 10x + y, where x and y are one's and ten's digits respectively


▶ According to the Question :


The sum of the digits of the number is 7


•°• x + y = 7 ....... ( i )


After reversing the digits, the number becomes 10y + x


The number formed by reversing the digit is 45 more than the original number


•°• 10y + x - ( 10x + y ) = 45


=> 10y + x - 10x - y = 45


=> 9y - 9x = 45


=> 9 ( y - x ) = 45


=> y - x = 5


=> x - y = - 5 ....... ( ii )


Adding eq ( i ) and ( ii ) , we get :


x + y = + 7


x - y = - 5

_____________________


2x = 2


x = 1


Substituting value of x in equation ( i ), we get :


x + y = 7


=> 1 + y = 7


=> y = 7 - 1


=> y = 6


•°• The number = 10x + y


= 10 × 1 + 6


= 10 + 6


= 16


✔✔ Hence, it is solved ✅✅


$\mathbb {\huge {\fcolorbox{yellow}{green}{Hope It Helps}}}$


$\huge\bf\red {\#BeBrainly}$

Answer 2

Answer:

→ The original number is 16 .

Step-by-step explanation:

Let the unit's digit of the original number be x .

And, the ten's digit of the original number be y .

Now, A/Q,

→ Sum of the two digits number is 7 .

∵ x + y = 7 ............(1) .

Original number = 10x + y .

Number obtained on reversing the digits = 10y + x .

A/Q,

→ The number obtained on reversing the digit is 45 more than the original number .

∵ 10x + y + 45 = 10y + x  .

⇒ 10x - x + y - 10y = - 45 .

⇒ 9x - 9y = - 45 .

⇒ 9( x - y ) = - 45 .

⇒ x - y = - 45/9 .

∵ x - y = -5 ...........(2) .

On substracting equation (1) and (2), we get

x + y = 7 .

x - y = -5 .

-  +     +

________

⇒ 2y = 12 .

⇒ y = 12/2 .

∴ y = 6.

On putting the value of 'y' in equation (1),  we get

∵ x + y = 7 .

⇒ x + 6 = 7 .

⇒ x = 7 - 6 .

∴ x = 1 .

Therefore , the original number = 10x + y .

= 10 × 1 + 6 .

= 10 + 6 .

= 16 .

Hence, the original number is 16 .

THANKS

#BeBrainly .