a number divided by 13 leaves a remainder 1 and if the quotient,thus obtained is divided by 5,we get a remainder of 3.what will be the remainder if the number is divided by 65

• let the no. be n
  By remainder theorem :-
  n=13q+1 -------------1 where q is quotient
  
  also given
  
  q=5t+3 -------------2 where t is quotient when q is divided by 5
  put the value of eq 2 in eq 1 we get
  
  n=65t + 40
  Therefore 40 is the remainder
• 7 years agoHelpfull: Yes(29) No(0)
• If you don't know any concept regarding a problem,try hit and trial method by taking examples.As we can see that when the quotient is divided by 5 we get remainder as 3,so the quotient can be 8,13 etc.put quotient as 8 and we already know remainder was 1 when the number was divided by 13,hence the number comes out to be 13*8+1=105.Hence one such number which satisfies all the criteria given above is 105.Now upon dividing it by 65,we get 40 as remainder and hence the answer.
• 7 years agoHelpfull: Yes(3) No(1)
• here d1=13 r1=1
  d2=5 r2=3
  when a number is divided by product of divisors , the remainder is d1(r2) + r1
  therefore remainder = 13*3 + 1= 40
• 7 years agoHelpfull: Yes(1) No(0)
• let N be the number.
  so,
  N=13*q+1
  N=5*q1+3
  
  N=1,14,27,40,53(by using n=13*q+1)
  N=3,8,13,18,23,,28,33,38,43,48,53(by using n=5*q1+3)
  
  common value is=53
  N=lcm(13,5)*q+53
  N=(65q+53)/65
  reminder =53
• 7 years agoHelpfull: Yes(1) No(2)
• N/13=1(rem.)......(1)
  N/5=3(rem.).........(2)
  N=13*Q+1>>>>>(3)
  put N value in 2 condition
  13*Q+1/5
  Q=3 then we get 40 but divisible by 65 (65>40)
  Q=8 then we get 105/65
  40(remainder)
• 5 years agoHelpfull: Yes(1) No(0)
• let the no. 105, divided by 13, we get remainder 1 & quotient 8, 8 will be divided by 5, we get 3 as a remainder, therefore, if we divide 105 by 65, we get 40 as a remainder.
  
  take another number, 170. divided by 13, we get remainder 1 & quotient 8, 8 will be divided
  by 5, we get 3 as a remainder, therefore, if we divide 105 by 65, we get
  40 as a remainder....
  
  40 is right answer.
• 6 years agoHelpfull: Yes(0) No(0)
• --> 13(5x + 3) + 1
  --> 65x + 40
  --> rem = 40
• 4 years agoHelpfull: Yes(0) No(0)