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?

1 Answer
Apr 6, 2018

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