The sum of the digits of a two digit number is 14. If 29 is substracted from the certain number, the newly formed number's digits are equal to each other. So, find the certain number.

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Solution

let the given number be xy
x+y=14⇒ x=14-y
xy-29=cc
⇒10x+y-29=10c+c. .............[we can write ab as 10a+b]
⇒10(14-y)+y-29=11c
⇒140-10y+y-29=11c
⇒111-9y=11c
111-9y should be an integral multiple of 11,this happens only when y=5
⇒x=14-5=9
so the number is 95

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