Question

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

Answer 1

Solution :-

Let the quantity of wine in the cask originally be x litres

8 litres of wine is drawn from it and replaced with water. his operation is performed 3 more times. It means this operation is done total 4 times.

After 4 operations -

Wine : Water = 16 : 65 or  Wine : Total = 16 : 81

⇒ [(x - 8)/x]⁴ = 16/81

⇒ [(x - 8)/x]⁴ = (2)⁴/(3)⁴

Powers are cancelled.

⇒ [(x - 8)/x] = 2/3

⇒ 2x = 3x - 24

⇒ 2x - 3x = - 24

⇒ - x = - 24

⇒ x = 24
 
So, originally the cask had 24 litres of wine.

Answer.