Question

11. A two digit number is four times the sum of the two
digits. If the digits are reversed, the number so
obtained is 18 more than the original number. What
the original number?
(a) 36 (b) 24 (c) 48 (d) 12​

Answer 1

Answer:

( b ) 24

Step-by-step explanation:

Given-----> Two digit number is four times the sum of the two digits , if the digits are reversed , the number so obtained is 18 more than the original number.

To find -----> Original number

Solution------> Let unit's and ten's place digits be x and y .

Original number = 10y + x

ATQ,

Two digit number = 4 × Sum of the two digits

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

=> 10y + x = 4x + 4y

=> 10y + x - 4x - 4y = 0

=> 6y - 3x = 0

=> 6y = 3x

=> 6y / 3 = x

=> 2y = x

On reversing the digits ,

New number = 10x + y

ATQ,

New number = Original number + 18

=> 10x + y = 10y + x + 18

=> 10x + y - 10y - x = 18

=> 9x - 9y = 18

Dividing whole equation by 9 .

=> x - y = 2

Putting x = 2y , in it , we get,

=> 2y - y = 2

=> y = 2

Now, x = 2y

Putting y = 2 , in it , we get,

x = 2 ( 2 )

=> x = 4

Original number = 10y + x

= 10 ( 2 ) + 4

= 20 + 4

= 24

So , option ( b ) is correct .