Question

a two digit number is 3 more than 4 times the sum of its digit .if 18 is added to the number, its digits are reversed.find the number​

Answer 1

Answer:

Required Number is 35

Step-by-step explanation:

Let the digit at unit's place be x

Let the digit at ten's place be y

Number = 10y + x

Given that number is 3 more than 4 times the sum of its digits

We have

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

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

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

-3x + 6y = 3

-x + 2y = 1 ---------- (1)

Also, given that if 18 is added to the number, its digits are reversed.

When digits are reversed, number = 10x + y

Thus, we get

10y + x  + 18 = 10x + y

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

9x - 9y = 18

x - y = 2 --------- (2)

Solving (1) and (2), we get

-x + 2y = 1

 x - y = 2

-----------------

y = 3

Putting y in (2),we get

x - 3 = 2

x = 2 + 3

x = 5

Thus, required number  = 10(3) + 5 = 35

Answer 2

Answer:

Step-by-step explanation:

let units digit be y adn tens be 10x

atq,

number=10x+y

∵

(10x+y) - 4(x+y)= 3.....(i)

and

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

Solving (i)

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

or,6x-3y=3

or,2x-y=1....(1)

Solving (ii)

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

or, 9y-9x=18

or,y-x=2...(2)

(1)+(2)

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

or,x=3

Thus, y=x+2 (from (2))

y=5

∴ the number= 10x+y=10x3+5=35