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 is 35

Answer 1

hi

let the number be xy

tens place = 10x and ones place = y

 
A two digit number is 3 more than 4 times the sum of its digits,

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

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

=> 3 = 10x -4x +y - 4y

=>3 = 6x - 3y

=> lets divide it by 3

=> 1 = 2x - y..[1]

=> y = 1 - 2x

if 18 is added to the number ,the digits are reversed 

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

=> 9x - 9y = 18

lets divide by 2

=>x - y = 2.[2]

letd add [1] and [2]

1 = 2x - y

x - y = 2

2x - y -x +y = 1 +2

=> 1x = 3

so x = 3

now 1 = 2x - y

=>1 = 2[3] - y

=>1 = 6 - y

=> y = 5

original no. = xy

=>x = 3 and y =5

=>35

hope it helps  u

:)

Answer 2

HELLO.......FRIENDS!!

THE ANSWER IS HERE,

Let the number be xy.

The expanded form of the number => 10x+y.

The number is 3 more than the 4 times the sum of its digit.

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

=> 10x+y=4x+4y+3.

=> 6x-3y=3.

=> 3 (2x-y)=3.

=> 2x-y =1....... (1)

If 18 is added the number will be reversed.

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

=> -9x+9y=18

=> 9 (-x+y)=18.

=> -x+y = 2........... (2)

Adding eq(1) & (2).

=> 2x-y-x+y=1+2.

=> x= 3.

Substitute the value of x in eq (1).

=> 2 (3)-y =1.

=> 6 -y =1.

=> y= 5.

So, The number will be..

=> 10x+y

=> 10 (3)+5.

=> 30+5.

=> 35.

:-)Hope it helps u.