Question

if m is equal to 77777......7777 is a 99 digit number and n is equals to 99999 ......99 is A 77 digit number .when sum of the digits in product M and n is equal to what?

Answer 1

n=1077−1n=1077−1

mn=77...779900...0077−77...7799mn=77...77⏟9900...00⏟77−77...77⏟99

mn=77...777700...002200...0077−00...002277..7777mn=77...77⏟7700...00⏟2200...00⏟77−00...00⏟2277..77⏟77

mn=77...7776699...9999+1−77...7777mn=77...77⏟76699...99⏟99+1−77...77⏟77

mn=77...7776699...992222...2277+1mn=77...77⏟76699...99⏟2222...22⏟77+1

mn=77...7776699...992222...22763mn=77...77⏟76699...99⏟2222...22⏟763

Sum of digits of mnmn

s(mn)=7⋅76+6+9⋅22+2⋅76+3s(mn)=7⋅76+6+9⋅22+2⋅76+3

s(mn)=9⋅76+6+9⋅22+3s(mn)=9⋅76+6+9⋅22+3 

s(mn)=9⋅76+9+9⋅22s(mn)=9⋅76+9+9⋅22

s(mn)=9⋅99s(mn)=9⋅99

s(mn)=891