Question

A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

Answer 1

Given : A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from 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 = 6(x + y) + 4

10y + x = 6x + 6y + 4

10y + x -  6x -  6y = 4

 -5x + 4y = 4

5x - 4y = - 4 ……………(1)

Condition : 2

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

10y + x - 10x -  y = 18  

- 9x + 9y = 18

-9(x - y) = 18

x - y = -18/9

x - y = - 2 …………..(2)

On multiplying equation (2) by 4 :  

4x - 4y = - 8 …………..(3)

On Subtracting equation (3)  from equation (1), we obtain :

5x - 4y = - 4

4x - 4y = - 8

(-)  (+)     (+)

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

x = 4

On putting x = 4 in eq (1)  we obtain :  

5x - 4y = - 4

5 (4) - 4y = - 4

20 - 4y = - 4

-4y = - 4 - 20

-4y = - 24

y = 24/4

y = 6

Now, Number = 10y + x = 10 × 6 + 4 =  60 + 4 = 64  

Hence, the number is 64.

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

 

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.

https://brainly.in/question/17181140

Answer 2

Answer:

Given:

⇏ A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed.

Find:

⇏ Find the number.

According to the question:

⇏ Let us assume 'x' as ones digit and 'y' as tens digit.

Calculations:

⇏ $\sf x + 10y = 6 \: (x+y)+4$

⇏ $\sf (x + 10y) = (6x+6y+4)$

⇏ $\sf 10y =( 5x+6y+4)$

⇏ ${\bf{\boxed{\bf{4y = 5x+4}}}}$

Subtracting 18 with the number:

⇏ $\sf (x+10y -18) =( y+10x)$

⇏ $\sf (10y -18) = (y+9x)$

⇏ $\sf 9y -18 = 9x$

⇏ ${\bf{\boxed{\bf{y -2 = x}}}}$

Adding values from above equations:

⇏ $\sf 4y = 5x+4$

⇏ $\sf 4y = 5 \: (y-2)+4$

⇏ $\sf 4y = 5y-10+4$

⇏ $\sf 4y = 5y-6$

⇏ $\sf 4y+6 = 5y$

⇏ ${\bf{\boxed{\bf{6 = y - - - Equation (1)}}}}$

Adding values from above equations:

⇏ $\sf 4y = 5x+4$

⇏ $\sf 4 \times 6 = 5x+4$

⇏ $\sf 24 = 5x+4$

⇏ $\sf 20 = 5x$

⇏ ${\bf{\boxed{\bf{4 = x - - - Equation (2)}}}}$

Therefore, value of xy = 64 and 64 is the number.