Question

1 Sum of digits of a two digit number is 8. If their digits are interchanged , the new number is increased by 18 than the original number. Find the original number.

Answer 1

Step-by-step explanation:

Given:

• Sum of digits of a two digit number
• If their digits are interchanged , the new number is increased by 18

To Find:

• The original number

Solution:

Let unit's digit be x

ten's digit=8-x

Original number=10(8-x)+x=80-10x+x=80-9x

Number after interchanging it's digits=10(x)+8-x

→10x+8-x=9x+8

The given is If their digits are interchanged , the new number is increased by 18. So if we add 18 to the original number then it is equal to its digits which are interchanged.

So,

ACQ

→9x+8=80-9x+18

→9x+9x=80+18-8

→18x=90

→x=5

Original number=80-9x=80-9×5=80-45=35