Find Smallest Number when divided by 7,8 and 9 leave remainder 5,4 and 2.

• 7a+5 = 8b+4 = 9c+2
  
  First take
  7a+5 = 8b+4
  7a = 8b-1
  Possible values of (a,b) satisfying the above eqn. is (1,1), (9,8),etc
  Take (1,1) = 7
  LCM(7,8)*n+12 [since 7a+5=8b+4=12]
  From (1) nd (2), we get 56n+12
  Now 56n+12 = 9c+2
  56n+10 = 9c
  "c" should be a multiple of "9".. So assign a value for n which satisfies the eqn...
  
  56*4+10 = 9c
  234/9 = c
  c = 26
  
  Substitute c=26
  9*26+2 = 236
  
  Hence 236 ...
  
• 10 years agoHelpfull: Yes(15) No(2)
• 236
  
  LCM(7,8,9)N+236
  504N+236
  Put N=0 to get the smallest value...
  
  Ans : 236
• 10 years agoHelpfull: Yes(1) No(2)
• Can u please explain how 236 came ??
  answer is 234(i guess). u can recheck and please elaborate if possible.
• 10 years agoHelpfull: Yes(0) No(0)
• Saraswathy.....i guess u preparing for CAT....and so do I....please can i connect with u on mail....please ping me on lovejeet0707@gmail.com if feasible to u....!
• 10 years agoHelpfull: Yes(0) No(0)
• for the problems like this..there is formulae
  N=k(d1d2d3)+(r1+r2d1+r3d1d2)
  N-number we need find
  k-constant from 0 to any integer
  d1,d2,d3 are divisors
  r1, r2, r3 are remainders
  here we need find smallest number ri8 then consider k=0
  so,
  N=(5+4*7+2*7*8)
  N=145
  IS D ANS
• 10 years agoHelpfull: Yes(0) No(0)
• 7a+5=8b+4=9c+2
  
  now b=(7a+1)/8--------------(1)
  
  and b=(9c-2)/8--------------(2)
  
  
  from eqn 1 the integral solutions of a & b:-
  
  a=1 b=1
  a=9 b=8
  a=17 b=15
  so b=1,8,15,...............(it is an A.P with d=7)------(3)
  
  from eqn 2 the integral solutions of b & c:-
  
  c=2 b=2
  c=10 b=11
  c=18 b=20
  so b=2,11,20,..............(it is an A.P. wiht d=9)------(4)
  
  from eqn 3 and eqn 4 we must get the value b same in both the eqns:-
  
  b=b
  
  --->1+(n-1)*7=2+(a-1)*9------(here n,a are any term of eqn3 and eqn4 respectively)-------(5)
  
  -->a=(1+7n)/9
  for lowest value of b we must get the lowest integral solution of n which is 5 and hence a=4
  
  thus putting n=5 or a=4 in eqn 4 we get b=29
  
  so the required number is 8b+4=236(ANS)
• 8 years agoHelpfull: Yes(0) No(0)