The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got `70000 less. Find the original price of the diamond.

a. 1.4 lakh
b. 2 lakh
c. 1 lakh
d. 2.1 lakh

• weight of total diamond=x+2x+3x+4x=10x
  so cost price of big diamond=(10x)^2=100x^2
  now when in pieces;
  total selling cost of pieces=x^2+(2x)^2+(3x)^2+(4x)^2=30x^2
  now
  loss=cp-sp;
  70000=(100-30)x^2;
  or 70x^2=70000;
  or x^2=1000
  
  henceoriginal cost=cost price=cp=100x^2=100000
  ans c)
• 10 years agoHelpfull: Yes(69) No(2)
• ans is 1 Lakh by hit and trial
  cost is directly propotional to square of weight total weight is 1+2+3+4=10
  so c=k*w^2
  10000=k*10*10 from here k=1000
  then
  c1=k*1^2=1000*1*1=1000
  c2=k*2^2=1000*4=4000
  c3=k*3^2=1000*9=9000
  c4=k*4^2=1000*16=16000
  total c1+c2+c3+c4=30,000 which is 70,000 less then 100,000 which is original cost.
• 10 years agoHelpfull: Yes(12) No(0)
• yo babay its 1 lakh u kknow
• 10 years agoHelpfull: Yes(3) No(7)
• Very Nice Question !!!
  
  answer is 100000
• 10 years agoHelpfull: Yes(2) No(0)
• Ans:1 lakh
  let price of diamond=x^2
  total price of 4 pieces=y^2(1+4+9+16)=30y^2
  weight is same x=(1+2+3+4)y=10y
  price of original diamond=(10y)^2=100y^2
  100y^2-30y^2=70000
  y^2=1000
  original price=100y^2=100(1000)=100000
• 10 years agoHelpfull: Yes(1) No(1)
• given four piece =1+2+3+4=10
  10pieces=100
  square of weight=1+4+9+16=30
  when sold =100-30=70
  70=70000
  1piece=1000
  100piece=100000
• 5 years agoHelpfull: Yes(0) No(0)