Question

✔️✔️50 points !!!✔️✔️

sum of the digits of two digit number is 9.the number obtained by inter changing the digit is 18 more than twice the original number the original number is :

a)72
B)27
C)63
d)36

❌❌NO SPAM ❌❌​​

Answer 1

Answer :-

27

Option → B

Given :-

Sum of digits of two digit number is 9.

The number obtained by interchanging digits is 18 more than twice the number.

Solution:-

Let the two digit number be 10x + y.

A/Q

→$x + y = 9 -----1)$

→$10y + x = 2(10x + y)+ 18$

→$10y + x = 20x+ 2y +18$

→$10y -2y = 20x -x +18$

→$8y-18 = 19x$

→$19x -8y = -18 ----2)$

• Multiplying eq.1 by 8.

→$8x + 8y = 72$

• Now add both equations.

→$19x +8x + 8y-8y = -18 +72$

→$27x = 54$

→$x = \dfrac{54}{27}$

→$x = 2$

• Put the value of x in eq.1

→$x + y = 9$

→$2 + y = 9$

→$y = 7$

Now,

The required original number is :-

→$10x + y$

→$10 \times 2 +7$

→$20+7$

→$27$

hence,

The original number is 27.

Answer 2

Answer:

Option => D.

The original number is 36.

Step-by-step explanation:

Given that :

The number obtained by inter changing the digit is 18 more than twice the original number.

Sum of the digits of two digit number is 9.

To Find :

The orignal number.

Solution :

$\textbf{\underline{\underline{Consider as - }}}$

⇒ Unit digit be - y

⇒ Tens digit be - x

So,

$\sf \implies Number\; formed = 10x + y\\ \\ \implies Reverse\;number = 10y + x$

$\sf \implies x + y = 9......Equation(1)\\ \\ \implies 10y + x = 10x + y + 27.......Equation(2)$

$\sf \implies 9y - 9x = 27\\ \\ \implies y - x = 3....Equation(3)$

Solving Equation 1 and 3 :

$\implies\sf x + y = 9\\ \\ \implies y - x = 3$

We get :

⇒ x = 3 and y = 6.

Hence,

Original Number = 36

Reversed Number = 63

$\textbf{\underline{\underline{Hence, The orignal number is 36. (Option = D)}}}$