The sum of a particular two digit number is 8. If this number's digits are reversed, the number is increased by 18. What is this number?

The sum of digits of a particular two digit number is 8. If this number's digits are reversed, the number is increased by 18. What is this number?

2 Answers
Mar 22, 2017

#35.#

Explanation:

A two digit no. has one digit in a #10's# place and one in a unit

place. Let these resp. digits be #x and y.#

Hence, the original no. is given by, #10xxx+1xxy=10x+y.#

Note that, we readily know that, #x+y=8...............(1).#

Reversing the digits of the original no., we get the new no.

#10y+x,# &, since, it is known that, this latter no. is #18# more than

the the original one, we have,

#10y+x=(10x+y)+18 rArr 9y=9x+18,#

# :. y=x+2........................(2).#

Subst.ing #y" from (2) into (1), "x+(x+2)=8 rArr x=3,#

# :." by "(2), y=x+2=5.#

Thus, the desired no. is #10x+y=35,#

Enjoy Maths.!

Mar 22, 2017

The original no. #35# and its "reverse," #53.#

Explanation:

As a Second Method, I would like to suggest the following

Solution with the help of Arithmetic.

Let us, observe that the Difference between a two digit no., and,

the one obtained by reversing its digits is #9# times the

Difference btwn. their digits.

For Example, consider a two digit no. #52#, and, its "reverse"

#25#, and, see that, #52-25=27=9(5-2).#

In our Problem, the difference of the no. and its "reverse" is #18#,

so, the Difference of the Digits must be #18-:9=2.........(1).#

Also, Sum of the Digits is given to be #8.....................(2).#

From #(1), and, (2),# we can easily conclude that the Digits

must be #1/2(8+2)=5 and, 1/2(8-2)=3,# giving the desired

original no. #35# and its "reverse," #53.#

Enjoy Maths.!