Question

please tell me the answer please

the sum of the digits of two digit number is 14 if the number formed by reversing the digit is less than the original number by 18 find the original numbers​

Answer 1

Answer:

Let the 2 digits be x and y.

This means that this is a two-digit number.

Given the sum of 2 digits =14.

⟹x+y−14=0………………..(1)

The number is 10x+y

x is in the tens place and y is in the units place.

To make this clear you can refer to the examples:-

73=7∗10+3

54=5∗10+4

67=6∗10+7

So :

10x+y is our assumed number.

Now if we reverse the number what it becomes?

Again few examples will clear your concept.

54⟹45

So 10x+y becomes 10y+x.

10∗5+4⟹10∗4+5

Now this becomes easier.

10x+y when reversed becomes 10y+x.

⟹10y+x=10x+y−18

⟹9y−9x+18=0

⟹x−y−2=0[ Dividing both sides by -9 ]……………(2)

Now adding equation (1) and (2) yields:-

x+y−14+x−y−2=0

⟹2x−16=0

⟹2x=16

⟹x=162

⟹x=8

Now x+y=14

⟹y=14−x

⟹y=14–8=6

Now original number is 10x+y

⟹10∗8+6

⟹80+6=86

The original number is 86.

Hope it helped you.