Question

from a vessel containing only 5 litres are drawn and replaced with water.this action is repeated once more.after this,the respective ratio of juice to water 81:19.how many litres of juice was the vessel originally holding​

Answer 1

If 5 litres of juice was drawn out and filled with water twice then the litres of juice that the vessel was originally holding was 50 litres.

Step-by-step explanation:

Let the original quantity of juice in the vessel be “x” litres.

Then, quantity of juice left in the vessel after 2 operations = x[1 – $\frac{5}{x}$]²

The new ratio of juice to water is given as = 81 : 19

Now, in order to get the original quantity of juice we will write an eq. as,

[Quantity of juice left in the vessel] / [Original quantity of juice in the vessel] = [New quantity of juice]/ [Total quantity of mixture]

∴ [x{1 – $\frac{5}{x}$}²] / x = $\frac{81}{81+19}$

⇒ {1 – $\frac{5}{x}$}² = $\frac{81}{100}$

Taking square roots on both sides

⇒ 1 – $\frac{5}{x}$ = $\frac{9}{10}$

⇒ $\frac{x-5}{x}$ = $\frac{9}{10}$

⇒ 10x – 50 = 9x

⇒ x = 50 litres

Thus, the the vessel originally was holding 50 litres of juice in it.

--------------------------------------------------------------------------------------

Also View:

Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.

https://brainly.in/question/6896448

8 litres are drawn from a cask full of wine and is then filled with water. this operation is performed three more times. the ratio of the quantity of wine now left in cask to that of water is 16 : 65. how much wine did the cask hold originally

https://brainly.in/question/2889409

In a vessel, there are 10 liters of alcohol. An operation is defined as taking out five liters of what is present in the vessel and adding 10 liters of pure water to it. What is the ratio of alcohol to water after two operations ?

https://brainly.in/question/11534267

Answer 2

Answer:

If 5 litres of juice was drawn out and filled with water twice then the litres of juice that the vessel was originally holding was 50 litres.

Step-by-step explanation:

Let the original quantity of juice in the vessel be “x” litres.

Then, quantity of juice left in the vessel after 2 operations = x[1 – \frac{5}{x}

x

5

²

The new ratio of juice to water is given as = 81 : 19

Now, in order to get the original quantity of juice we will write an eq. as,

[Quantity of juice left in the vessel] / [Original quantity of juice in the vessel] = [New quantity of juice]/ [Total quantity of mixture]

∴ [x{1 – \frac{5}{x}

x

5

}²] / x = \frac{81}{81+19}

81+19

81

⇒ {1 – \frac{5}{x}

x

5

}² = \frac{81}{100}

100

81

Taking square roots on both sides

⇒ 1 – \frac{5}{x}

x

5

= \frac{9}{10}

10

9

⇒ \frac{x-5}{x}

x

x−5

= \frac{9}{10}

10

9

⇒ 10x – 50 = 9x

⇒ x = 50 litres

Thus, the the vessel originally was holding 50 litres of juice in it.