Question

14.5 litres of wine replaced from a filled
container of oil and filled with water.
It is repeated again. Now the ratio
of wine and water becomes
25 : 11. Find the capacity of the
container
[NET, 1998]​

Answer 1

Answer:

5 litres of wine is replaced from a filled container of oil and filled with water. It is repeated again. Now the ratio of wine and water becomes 25:11. What is the capacity of the container?

6 Answers

Sushil Parwani, former Retired Since 2014

Answered 10 months ago · Author has 1K answers and 67.8K answer views

How is wine removed from a container of OIL?

However assuming it is a container of wine with capacity x

After removing 5 litres of wine and replacing with 5 litres water container x-5 litres wine and 5 litres water.

when process is repeated

wine removed (x-5)/x .5=5-25/x

wine left=(x-5)-5+25/x=x-10+25/x

water in container=x-wine left

=10–25/x

Ratio wine to water=(x-10+25/x)/(10–25/x)=25/11

(x-10+25/x).11=(10–25/x) .25

(x^2–10x+25).11=(10x-25).25

11x^2–110x+275=250x-625

11x^2–360x+900=0

x= 30 litres

other value 30/11 is neglected as it is less than 5 litres and 5 litres are to be drawn out

Answer 2

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Let the capacity of the wine container or the original quantity of wine in the container be X

Then the quantity of wine left in the container after two operations = x[$1 - \frac{5}{x}$]²

The new ratio of wine to water is given as 25:11

Now, in order to get the quantity of wine we will write an equation as

$\frac{ quantity \: \: of \: \: wine \: \: left \: \: in \: \: the \: \: vessel}{original \: \: quantity \: \: of \: \: wine \: \: in \: \: the \: \: vessel } = \frac{new \: \: quantity \: \: of \: \: wine}{ total \: \: quantity \: \: of \: \: mixture }$

$\frac{[x(1 - \frac{5}{x} {}^{2} ]}{x} = \frac{25}{25 + 11} \\ \\ {(1 - \frac{5}{x} )}^{2} = \frac{25}{36} \\ \\ taking \: \: square \: \: roots \: \: both \: sides \: \: \\ \\ 1 - \frac{5}{x} = \frac{5}{6} \\ \\ 6(x - 5) = 5x \\ \\ 6x - 30 = 5x \\ \\ 6x - 5x = 30 \\ \\ x = 30 \: \: litres$

Thus, capacity of wine container is 30 litres