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Find-a-number-that-becomes-N-times-smaller-if-the-first-digit-is-removed-in-the-following-cases-1-N-17-2-N-27-3-N-37-4-N-47-




Question Number 99058 by Learner-123 last updated on 18/Jun/20
Find a number that becomes N times  smaller if the first digit is removed  in the following cases:  1) N=17  2) N=27  3)N=37  4)N=47.
FindanumberthatbecomesNtimessmallerifthefirstdigitisremovedinthefollowingcases:1)N=172)N=273)N=374)N=47.
Commented by Rasheed.Sindhi last updated on 18/Jun/20
1) N=17
1)N=17
Commented by mr W last updated on 18/Jun/20
i don′t understand what is meant.  say the number is XYYYYY.  it should be  YYYYY=((XYYYYY)/N) with N=17?
idontunderstandwhatismeant.saythenumberisXYYYYY.itshouldbeYYYYY=XYYYYYNwithN=17?
Commented by Rasheed.Sindhi last updated on 18/Jun/20
Sir I understand by first digit  ′unit-digit′.So if remove 7 from  17 it becomes 1which is 17 times  smaller than 17.
SirIunderstandbyfirstdigitunitdigit.Soifremove7from17itbecomes1whichis17timessmallerthan17.
Commented by mr W last updated on 18/Jun/20
thanks sir!  (Xy)=10X+y=17X  ⇒y=7X≤9  ⇒X≤(9/7) ⇒X=1 ⇒y=7  ⇒the number is 17.    (Xy)=10X+y=27X  ⇒y=17X≤9 ⇒X≤(9/(17)) ⇒no solution
thankssir!(Xy)=10X+y=17Xy=7X9X97X=1y=7thenumberis17.(Xy)=10X+y=27Xy=17X9X917nosolution
Commented by Learner-123 last updated on 18/Jun/20
thanks both sirs!
thanksbothsirs!
Commented by Rasheed.Sindhi last updated on 18/Jun/20
First-digit(unit-digit)removing:  tu=10t+u→(((10t+u)−u)/(10))=u  (((10t+u)−u)/(10))=((10t+u)/(10t+u))=1  t=1  The required number is 1u  11,12,13,...,19
Firstdigit(unitdigit)removing:tu=10t+u(10t+u)u10=u(10t+u)u10=10t+u10t+u=1t=1Therequirednumberis1u11,12,13,,19

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