Question

A 2 digit no is 3 more than 4 times the sum of its digits. If 18 is added to the no, the digits interchange their places.

Answer 1

Let the number be 10x+y
10x+y=4(x+y)+3
6x-3y=3
2x-y=1-------------(i)

10x+y+18=10y+x
9y-9x=18
y-x=2---------------------(ii)
Solve the equations,
x=3, y=5
So, Original number is 35.

Answer 2

let, the the two digits are X and Y and the number is XY that is (10X + Y)

now, a/c to question,

(10x + y) =4(x + y) +3
=> 6x -3y = 3 ..............eq.(1)

also, when we add 18 then the digitsinterchange their position that is

(10x + y) +18 = (10y +x)
=> 9x -9y +18 =0
=> -9(y- x -2) = 0
=>y-x = 2
=>y = 2+x
now put this value in eq.(1)

=>6x -3(2+x) = 3
=> 3x =3+6
=> x = 3
and y = 3+2 = 5

Hence the number is (3×10 + 5) = 35
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Hope it it helps.........