Question

A two digit number 3 times more than 4 times the sum of its digit . If 18 is added to the number the digits are interchanged . Find the number .

Answer 1

let us take the ten's digit be 'x'
let us take the unit digit be 'y'
so, the number will be "10x+y"
number formed by reversing this = "10y+x"
according to question
10y+x=4(x+y)+3
10y+x=4x+4y+3
10y+x-4x-4y=3
10y-4y+x-4x=3
6y-3x=3
3(2y-x)=3
2y-x=1..............(1)
it is also given in the question if 18 is added to the no. the Digits are interchanged
hence,
(10y+x)+18=10x+y
10y+x+18=10x+y
18=10x+y-10y-x
18=9x-9y
9x-9y=18
9(x-y)=18
x-y=18/9
x-y=2...........(2)
adding equation (1)&(2)
2y-x+x-y=1+2
2y-y=3
y=3........(3)
put equation (3) in equation (2)
x-y=2
x-3=2
x=2+3
x=5
hence, the number will be
10x+y
10*5+3
50+3
53

Answer 2

Answer:

53

Step-by-step explanation:

Let tens digit be = x

then , units digit = y

number = 10x + y

reversed number = 10y + x

Given ,  

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

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

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

6y - 3x = 3

2(2y - x) = 3

2y - x = 3--------1

second part of the question says -

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

10y - y + x - 10x = 18

9y - 9x = 18

9 ( y - x ) = 18

y - x = 18 / 9

y - x = 2---------2

Now we should add the equation 1 and 2

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

2y-y=3

y=3........(3)

put equation (3) in equation (2)

x-y=2

x-3=2

x=2+3

x=5  

hence, the number will be  

10x+y

10*5+3

50+3

53

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