The cost of two varieties of paint is Rs.3969 per 2 kg and Rs.1369 per 2 kg respectively. After how many years will the value of both paint be the same, if variety1 appreciates at 26% per annum and variety2 depreciates at 26% per annum?

• Assuming variety1 depreciates and variety2 appreciates....
  
  If the value P depreciates at the rate of R% per annum then after n years it becomes =
  P x (1 - R/100)^n
  And if the value of P appreciates at the rate of R% per annum then after n years it becomes =
  P x (1 + R/100)^n.
  
  Let the required time be n years.
  Given that, the cost of variety1 is Rs.3969 and depreciates at the rate of 26% per year.
  Therefore, the cost of variety1 after n years = P x (1 - R/100)^n
  = 3969 x (1- 26/100)^n
  = 3969 x (74/100)^n ...(1)
  
  And, the cost of variety2 is Rs.1369 and appreciates at the rate of 26% per year.
  Therefore, the cost of variety2 after n years = P x (1 + R/100)^n
  = 1369 x (1+ 26/100)^n
  = 1369 x (126/100)^n ...(2)
  
  From the given condition, we have (1) and (2) are equal.
  i.e., 3969 x (74/100)^n = 1369 x (126/100)^n
  
  3969/1369 = (126/74)^n
  (63/37)^2= (63/37)^n
  n = 2.
  
  Hence the required answer is 2 years.
• 9 years agoHelpfull: Yes(21) No(0)
• acc to ques 3969(1-26/100)^n=1369(1+26/100)^n
  on solvin 3969/1369=(126/74)^n
  (63/37)^2=(63*2/37*2)^n
  so n=2
• 9 years agoHelpfull: Yes(6) No(0)
• Simply appreciates variety1 by 26% and depreciates variety2 by 26% as:
  
  Var1 var2
  3969.00 1369 initially
  2937.06 1724.94 after I year
  2173.42 2173.42 after II year
  
  so the price become same after 2 years
• 9 years agoHelpfull: Yes(3) No(0)
• No,the cost of both the paints will never be same.(if it is wrong please suggest me)
• 9 years agoHelpfull: Yes(2) No(6)