Question

When you reverse the digits in a certain two-digit number you decrease its value by 18. Can you find the number if the sum of its digits is 10?

Answer 1

Number are :64,46 viz 6 and 4

Explanation:

Let two digits regardless of their place value be 'a' and 'b'.
Given in question sum of their digits regardless of their position is 10 or `a+b=10` Consider this is equation one,
`a+b=10`...... (1)

Since its a two digital number one must be 10's and another must be 1s. Consider 'a' be the 10's and b be the 1s.
So
`10a+b` is the first number.
Again their order is reversed so 'b' will turn into 10's and 'a' will turn into 1s.
`10b+a` is the second number.

If we do so we decrease the first number by 18.
So,
`10a+b-18=10b+a`
`or, 10a-a+b-10b=18`
`or, 9a-9b=18`
`or, 9 (a-b)=18`
`or, (a-b)=(18/9)`
`or, (a-b)=2`...... (2)

Solving equation (1) and (2)
`a+b=10`... (1)
`a-b=2`... (2)

In equation (2).
`a-b=2`
`or, a=2+b`

Substitute in equation (1).
`a+b=10`
`or, 2+b+b=10`
`or, 2+2b=10`
`or, 2 (1+b)=10`
`or, 1+b=(10/2)`
`or, 1+b=5`
`:.b=5-1=4`

Re substitute in equation (1)
`a+b=10`
`or, a+4=10`
`:.a=10-4=6`

The numbers are `4` and `6`