professor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?

• find out the common term in those 3 series for (2,4,8)
  3N+2=2,5,8,11,14......71,74
  7N+4=4,11,18...67,74
  11N+8=8,19,30......63,74
  find out the common term in those 3 series for (2,5,4)
  3N+2=2,5.....23,26
  7N+5=5,12,19,26
  11N+4=4,15,26
  now 74-26=48
• 9 years agoHelpfull: Yes(27) No(2)
• how did you get 74 and 26..plz explain
• 9 years agoHelpfull: Yes(3) No(2)
• answer is 48
• 9 years agoHelpfull: Yes(2) No(12)
• plz explain how u got 74 and 26
• 9 years agoHelpfull: Yes(1) No(1)
• for (2,4,8)
  N=3q+2,substitute q=0,1,2,3,4........ so we get 2,5,8,11,......74
  N=7q+4 =4,11,18,......74
  N=11q+8=8,19,.....74
  common no in above 3 eqs is 74
  like wise u do for (2,5,4)
  here we get 26
  then money left in purse is 74-26=48
• 8 years agoHelpfull: Yes(1) No(0)
• Let the money with the professor = N
  Then N = 3a +1 = 5b + 1 = 7c + 6.
  Solving the above we get N = 181
  (Explanation: See LCM formula 1 and 2: Click here)
  When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.
  In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.
  ⇒ 15x + 1 = 7c + 6 ⇒ c = 15x−5715x−57 ⇒ c = 2x+x−572x+x−57
  Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.
  (x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)
  Similarly Money given to servant = M = 3x + 2 = 5y = 7z + 6
  Solving we get M = 25.
  (125 also satisfies but this is next number)
  Now N - M = 56
  
• 8 years agoHelpfull: Yes(1) No(1)
• remembers(2,4,8)
  paid (2,5,4)
  (2,4,8)-(2,5,4)=(0,-1,4)
  48/3=0
  48/7=-1
  48/11=4
  
  ans:48
• 6 years agoHelpfull: Yes(1) No(0)
• (2,4,8)=74
  (2,5,4)=26
  money left in the pocket=74-26=48
• 9 years agoHelpfull: Yes(0) No(3)
• (2,4,8)=74 & (2,5,4)=26
  so ,74-26=48
  therefore 48 is the answer
• 9 years agoHelpfull: Yes(0) No(2)
• answer is 48
• 9 years agoHelpfull: Yes(0) No(1)