Re: Five liters are taken off from a vessel full of water and replaced wit
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14 Jan 2023, 03:18
Five liters are taken off a vessel full of water and replaced with pure milk. Again, five more liters of the mixture is taken and replaced with pure milk After this process, if the vessel contains water and milk in the ratio 9:16 what is the vessel's capacity?
Let's say the total volume of the vessel is x Liter
Step1: Five liters are taken off from a vessel full of water and replaced with pure milk, therefore
water = (x-5) ltr
milk = x ltr
Ratio = (x-5)/x
Step2: Again, five more liters of the mixture are taken and replaced with pure milk
{{{To understand this, let's take one easy example, let's say we have a solution of 2 ltr of coke and 5 ltr of water that's sum up to 7 ltr of the solution if we remove 3 ltr from the solution, then 3 ltr will reduce this solution in the ratio 2:5, 2 part of coke will get reduce and 5 part of water will get reduce, so total coke removed = (2/7)*3 and similarly total water reduced = (5/7)*3. }}}
back to the original question
Hence, removing 5 ltr from the above solution
Total part of water removed = 5(ltr)* (x-5)/x
Total part of milk removed = 5(ltr)* 5/x
So current status of the solution
Water = (x-5) - 5*(x-5)/x
Milk =5 - 5*5/x +5(addition 5 ltr of milk added)
So on further solving water to milk ratio will become = (x^2-10x+25)/(10x-25) = 9:16,
on further solving, you will get two solutions for this quadratic equation, 16x^2-250x+625=0
x= 12.5 and x = 4.125 (not possible, since original vessel should be greater than 5ltr)
So the volume of the vessel =12.5 ltr.