Question

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

Answer 1

Let the first digit be x and the second digit be y.
Then, the number will be 10x+y.
Acc. to the question, 10x+y = 4*(x+y)+3
10x-4x + y-4y = 3
6x - 3y = 3 Divide this by 3 we get,
2x-y=1. (1)
Also, 10x+y+18 = 10y+x
10x-x+y-10 = -18
9x-9y = -18
Divide this by 9 we get,
x-y=-2. (2)
On doing (1) - (2) We get,
x = 3.
Then, y = x +2
y=3+2
y = 5.
Therefore, the number is 35.
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Answer 2

let the tens digit be x and ones digit be y
original number =10x+y
so equation 1 is
6x-3y=-3
reverse number =10y+x
equation 2 is
9x-9y=-18
on adding equation 1 &2 we get
x=7
putting the value of x in equation 1 we get
6x-3y=-3
6*7-3y=-3
42-3y=-3
42+3=3y
3y=45
y=45/3
y=15