In number system 541 * 21 =20222 , find 421 in decimal number system

• the no. in x digit no. in N th base would be
  n=N^x-N^(x-1)
  so
  541*21= 11361(5 digit no.)
  20222(five digit no.)
  so by formula
  5=N^5-N^4;
  5=N^4(N-1)
  so if N-1=5
  N=6
  So base would be 6
  now we have to convert 421 to decimal
  so
  4*6^2+2*6+1*6^0
  =144+12+1
  =157
  bhai yahi hoga answer
  
• 11 years agoHelpfull: Yes(11) No(5)
• pls can any one explain this
  
• 11 years agoHelpfull: Yes(3) No(0)
• formation of nos.btwn 100 and 200
  101
  110 112
  121 123
  132 134
  143 145
  154 156
  165 167
  176 178
  187 189
  198
  so total 18 nos. btwn 100 and 200 hundred (see pattern of the above nos. its simple)
  now from 201 to 300
  202
  211 213
  220 224
  231 235
  242 246
  253 257
  264 268
  275 279
  286
  297
  so total 17 nos. btw 201 and 300. see last two rows decreasing
  hence similarly btw 301 to 400 one more no will decrease in the row btwn 370 to 380 leading to total of 16 nos in btw 301 to 400.
  so total sum =18+17+16= 51
  it's correct
• 11 years agoHelpfull: Yes(2) No(0)
• here the no given that is
  
  541 and 21 both are of the same base as of the no 20222 is,so
  
  firstly find the base
  which is given by formula with x digit no. in N base
  
  n=N^x-N^(x-1)
  here the digit having 5 no. so
  
  5=N^4(N-1)
  
  so N-1=5
  N=6
  
  After converting the numbers in decimal number system
  the actual no are
  206*13=2678
  
  
  so similarly converting the given no. in decimal no. system
  
  4*6^2+2*6^1+1*6^0
  
  which gives no as
  
  157
• 9 years agoHelpfull: Yes(2) No(0)
• which type que. is this can anybdy explain it?
• 11 years agoHelpfull: Yes(1) No(0)
• SOMETHING WRONG IN QUESTION. Unit digit must be 1.
• 11 years agoHelpfull: Yes(1) No(2)
• 17702
  541-421*21
  
• 11 years agoHelpfull: Yes(1) No(1)
• i think the questn is like 542 * 21 =20222 , find 421 in decimal number system?
  
  from the given numbers we can find the base =6
  so 421 in decimal will be 111.
• 11 years agoHelpfull: Yes(1) No(1)
• Question is wrong .
  541 base 6 = 205 base 10
  21 base 6 = 13 base 10
  
  205 * 13 = 2665 base 10
  
  now converting base 10 to base 6 means
  2665 base 10 = 20201 base 6
  
  show this question is wrong.
• 7 years agoHelpfull: Yes(1) No(0)
• @shivangi
  r u sure abt the questn.
  unit digit of either 541 or 21 should be 2
  or
  unit digit of rhs should be 1
• 11 years agoHelpfull: Yes(0) No(0)
• pls yr solve this
  
• 11 years agoHelpfull: Yes(0) No(1)
• no clarity in que......
  
• 11 years agoHelpfull: Yes(0) No(1)