Question

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

Answer 1

Given :A two-digit number is 3 more than 4 times the sum of its digits. If 8 is added to the number, the digits are reversed.  

Solution:

Let the digit in the unit's place be x and the digit at the tens place be y.

Number = 10y + x

The number obtained by reversing the order of the digits is = 10x + y

 

ATQ :

Condition : 1

10y + x = 4(x + y) + 3

10y + x = 4x + 4y + 3

10y +  x - 4x -  4y = 3

6y - 3x = 3

-3x +  6y = 3

-3(x - 2y) = 3

x - 2y = - 3/3

x - 2y = -1……………(1)

Condition : 2

(10y + x) + 18 = 10x + y

10x + y - 10y - x = 18

9x - 9y = 18

9(x - y) = 18

x - y = 18/9

x - y = 2 …………..(2)

On Subtracting equation (2)  from equation (1), we obtain :

x - 2y = - 1

x - y = 2

(-)  (+)     (-)

------------------

-y = - 3

y = 3

On putting y = 3 in eq (1)  we obtain :  

x - 2y = - 1

x - 2 × 3 = - 1

x - 6 = - 1

x = - 1 + 6

x = 5

Now, Number = 10y + x = 10 × 3 + 5 =  30 + 5 = 35  

Hence, the number is 35.

Hope this answer will help you…

 

Some more questions from this chapter :  

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

https://brainly.in/question/17178564

 

The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

https://brainly.in/question/17177587

Answer 2

Answer:

Given:

⇏ A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed.

Find:

⇏ Find the number.

According to the question:

⇏ Let us assume 'x' as tens place and 'y' as unit place.

Calculations:

Case (1)

⇏ $\sf 10x + y=4 \: (x+y)+3$

⇏ $\sf 10x+y=4x+4y+3$

⇏ $\sf 10x-6x+y-4y=3$

⇏ $\sf 4x-3y=3$

⇏ ${\bf{\boxed{\bf{ 2x-y=1 - - - Equation(1)}}}}$

Case (2)

⇏ $\sf 10x+y+18=10y+x$

⇏ $\sf 10x-x+y-10y=-18$

⇏ $\sf 9x-9y=-18$

⇏ ${\bf {\boxed{\bf{x-y =-2\: - - - Equation (2) }}}}$

Case (3)

Case (3) Subtracting Equation (2) from (1)

⇏ $\sf (x-y)(-2x-y)=-2-1$

⇏ $\sf -x-y-2x-y=- 2-1$

⇏ $\sf -x=-3$

⇏ ${\bf{\boxed{\bf{ x=3}}}}$

⇏ $\sf 2x-y=1$

⇏ $\sf 2\times3-y=1$

⇏ $\sf 6-y=1$

⇏ ${\tt{\boxed{\tt{-y=-5}}}}$

Finding the numbers:

⇏ $\sf (10x+y) =(10\times3+5)$

⇏ ${\tt{\boxed{\bf{35}}}}$

Therefore, 35 is the number.