Question

A two-digit number is 3 more than 4 times the sum of it's digits. if 18 is added to the number, it's digit will be reversed. find the number.

Answer 1

Answer:

Step-by-step explanation:

let the digits are x y

no=10x+y

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

6x-3y=3

2x-y=1

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

10x+y+18=x+10y

9x-9y=-18

x-y=-2

x-2x+1=2

-x=-3

x=3

y=2*3-1=5

no is 35

Answer 2

The number is 35

Given :

The two digit number is 3 more than 4 times the sum of it's digits :-

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

If 18 is added digits reversed :-

$10x + y + 18 = x + 10y$

Solution :-

As by given ,

$\implies10x + y = 4(x + y) + 3$

$\implies10x + y = 4x + 4y + 3$

$\implies10x - 4x - 4y + y = 3$

$\implies(6x - 3y = 3) \div 3$

$\implies2x - y = 1$

$\implies \: y = 2x - 1...(1)$

It's given after adding 18 in both sides the equation be alike,

$\implies \: 10x + y + 18 = x + 10y$

$\implies \: 10x - x - 10y + y = - 18$

$\implies \: (9x - 9y = - 18) \div 9$

$\implies \: x - y =- 2 \: (substitute(1))$

$\implies \: x - (2x - 1) = - 2$

$\implies \: - x + 1 = -2$

$\implies \: x = 3$

we know that

$y = 2x - 1 \\ y = 2(3) - 1 \\ y = 6 - 1 \\ y = 5$

Hence the number is 35