Question

please give the answer
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

Let the two digit no. be (10x + y).

According to the question,

10x + y = 4 + 6 (x + y)

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

4x = 4 + 5y

4x - 5y = 4...................1

No. formed when digits are Reversed = 10y + x

According to the question,

10x + y - 18 = 10y + x

9x - 9y = 18

x - y = 2................….2

On multiplying eq 2 by 4 , we get

=> 4x - 4y = 8...........…..3

On subtracting eq 1 and 3 , we get

=> y = 4

Now, substituting the value of y in eq 2, we get

x - y = 2

x - 4 = 2

Therefore x = 6

Original number = 10x + y

= 10 × 6 + 4

= 64

Ans. = The number is 64.

Hope it helps!! :D

Answer 2

Solution :

The number interchanges after subtracting '18' ...
=> ( 10x + y ) - 18 = ( 10y + x )
=> ( 9x - 9y ) = 18
=> ( x - y ) = 2

-> ( 10x + y ) = 6( x + y ) + 4
=> ( 4x -5y ) = 4

From the two equations : [ x = 6 ; y = 4 ]
=> The number is 64 √√