In what ratio must a person mix 3 kinds of tea costing rs 60/kg, 75/kg, 100/kg so that the resultant mixture when sold at 96/kg yields a profit of 20 %

ans is 1:4:2
is there any cross method short cut for such kind of problem??? pls help

• The resultant mixture is sold at a profit of 20% at Rs.96/kg
  i.e. 1.2 (cost) = Rs.96 => Cost = = Rs.80 / kg.
  The best way to solve a problem of this kind is to go from the answer choices
  The resultant ratio QA : QB : QC :: 1 : 4 : 2.
  1 kg of variety A at Rs.60 is mixed with 4 kgs of variety B at Rs.75 and 2 kgs of variety C at Rs.100.
  The total cost for the 7 kgs = 60 + (4 * 75) + (2 * 100) = 60 +300 + 200 = 560.
  Cost per kg of the mixture = 560/7 = 80 kgs
• 9 years agoHelpfull: Yes(24) No(13)
• 96/kg yields a profit of 20%
  take an example selling price=100%+profit 20%
  100/120=5/6
  5*96/6=480/6=80
  cost=80rs/kg
  
  apply option to we can get esly ans...
  
  1:4:2
  (60*1)+(75*4)+(100*2)=60+300+200=560
  560/(1+4+2)=80
  
  80==80 Ans !!!!...
  
  
  
• 9 years agoHelpfull: Yes(18) No(0)
• this problem can only be solved by using hit and trial using the options
  
  given,
  s=96 rs/kg
  profit= 20%
  i.e. 20% of cost price
  
  p= 20/100 * cp
  p= cp/5
  
  
  wkt,
  s=p+c
  
  96=c/5 +c= 6/5 c
  
  c= (96*5)/6= 80rs/kg
  
  CONSIDERING PRICE--->
  we can write,
  
  k(60k +75y +100z)=80 ...(B)
  
  CONSIDERING WEIGHT-->
  for 1 kg of required mixture,
  k(x+y+z)=1 [taking k as proportionality consatnt]
  k=1/(x+y+z)..(A)
  
  
  
  now, if we substitute the option 1:4:2,
  
  using (A),
  k=1/(1+4+2)
  k=1/7
  
  and now using (B),
  1/7(60+300+200)=80
  1/7 * 560=80
  80 =80
  
  hence, our assumpstion for the option 1:4:2 is correct
  
  
• 9 years agoHelpfull: Yes(7) No(0)
• go through options
  for ex:-1:4;2 than cost is =1*60+4*75+2*100=560
  than 560*120/100=720
  which satisfy the question
• 9 years agoHelpfull: Yes(1) No(0)
• The resultant mixture is sold at a profit of 20% at Rs.96/kg
  i.e. 1.2 (cost) = Rs.96 ⇒ Cost =96/1.2=Rs.80 / kg.
  
  Let the three varieties be A, B, and C costing Rs.60, Rs.75 and Rs.100 respectively.
  
  The mean price falls between B and C.
  
  Hence the following method should be used to find the ratio in which they should be mixed.
  
  Step 1:
  Find out the ratio of Qa:Qc
  using alligation rule:
  Qa/Qc=(100−80)/(80−60)=1/1
  
  Step 2:
  Find out the ratio of Qb:Qc
  using alligation rule:
  Qb/Qc=(100−80)/(80−75)=4/1
  
  Step 3:
  Qc, the resultant ratio of variety c
  can be found by adding the value of Qc in step 1 and step 2=1+1=2
  The resultant ratio Qa:Qb:Qc::1:4:2
  
  
• 8 years agoHelpfull: Yes(0) No(0)