The sum of the digits of a two-digit number is 10. If the digits are reversed, a new number is formed. The new number is one less than twice the original number. How do you find the original number?

1 Answer
Alan N.
May 21, 2018

Original number was #37#

Explanation:

Let #m and n# be the first and second digits respectively of the original number.

We are told that: #m+n=10#
#-> n=10-m# [A]

Now. to form the new number we must reverse the digits. Since we can assume both numbers to be decimal, the value of the original number is #10xxm+n# [B]

and the new number is: #10xxn+m# [C]

We are also told that the new number is twice the original number minus 1.

Combining [B] and [C] #-> 10n+m = 2(10m+n)-1# [D]

Replacing [A] in [D]

#-> 10(10-m)+m = 20m +2(10-m)-1#

#100-10m+m=20m+20-2m-1#

#100-9m = 18m+19#

#27m = 81#

#m=3#

Since #m+n =10 -> n=7#

Hence the original number was: #37#

Check: New number #=73#

#73 = 2xx37-1#

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