A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?
a) 13 b) cannot be determined c) 3 d) 42

• making eqn as per the question
  a=Dx+8......1
  a=3Dy+21....2
  multiplying 3 in eqn 1 we get eqn 3
  3a=3Dx+24....3
  a=3Dy+21......2
  now subtract 2 from 3 we get..
  2a=3D(x-y)+3
  so here's the remainder we got is 3
  so is the answer option c
• 13 years agoHelpfull: Yes(145) No(5)
• 1)?assume D=13, we need remainder as 8 so 21/13=8 remainder.
  2)then 3D leaves the remainder 21, so 21/3*13=21/39=21.
  3)twice the remainder of 2 is divided by 3D, so 42/3*13=42=39=3
• 13 years agoHelpfull: Yes(16) No(7)
• analytic way as abhove one is very good trick
  n=kD+8,D>8
  n=3mD+21
  subtract
  we get,
  d=13/k-3m
  which is satify for d integer is (1,0)&(4,1)
  choosing 1,0
  D=13
  ans=3
  while chosin 4,1
  ans=8
  option given 3
  so 3is ans
  
• 13 years agoHelpfull: Yes(7) No(2)
• Remainder = 3
  let number is x,and quotient is A . D is divisor,and R is remainder= 8
  then x = A*D + 8 --------------(I)
  in second situation let quotient is B , 3D is divisor and R is remainder = 21
  then x = B*3D +21 -----------(II)
  from eq.(i)& eq.(ii)
  AD +8 =3BD +21
  or AD - 3BD =21 - 8 = 13
  or D (A- 3B) =13*1
  or D=13 ,and A -3B = 1 , IF B = 1 ,then A = 4
  NUMBER X = 4*13 + 8 = 52+8 = 60
  If 60*2 is divided by 3D =3*13 =39,
  120/39 = 3 is quotient,and REMAINDER = 3 ANS.
• 13 years agoHelpfull: Yes(6) No(3)
• @baidyanath............ hai dude hav some dout........ equation for d will be satified for diffrent solution resulting it as integer u can try for (1,0)(4,1)(7,2) (10,3) and many more which gives on simplification of 2*x/3*d gives us 42/39 , 2.999, 198/39, 276/ 39...... as the values changing we will et several solution in which 2.99 will be some wht neare ........... i wil accept C..... but i think we cannot be determined is also acepted wht u wil say......?????
• 13 years agoHelpfull: Yes(3) No(4)
• by making the equations,
  q=dx+8
  q=3dy+21
  by multiplying the equation 1 by 3 and substracting it with 2 eqn we get remainder as 3
  
• 10 years agoHelpfull: Yes(1) No(1)