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A chemical solution appears green when the salt concentration is 8 grams per litre (gpl) and red when it is 10 gpl. Pure water was added to the solution of 1 litre of 15 gpl solution till it turned green. Then 125 ml of the green solution is taken out and x grams of salt is added to the green solution to make it red. Another 500 ml of the final solution was taken out and y litres of green solution is added to get a resultant solution of concentration 9.6 gpl.  Assume adding salt doesn’t change its volume and find the ratio of x and y. 

A chemical solution appears green when the salt concentration is 8 grams per litre (gpl) and red when it is 10 gpl. Pure water was added to the solution of 1 litre of 15 gpl solution till it turned green. Then 125 ml of the green solution is taken out and x grams of salt is added to the green solution to make it red. Another 500 ml of the final solution was taken out and y litres of green solution is added to get a resultant solution of concentration 9.6 gpl.  Assume adding salt doesn’t change its volume and find the ratio of x and y.  Correct Answer 2

125 ml of green solution is taken

⇒ It contains 125 ml × 8 gpl = 1 g of salt

⇒ 125 ml of red solution contains 125 × 10 gpl = 1.25 g of salt

The extra salt added, x = 1.25 – 1 = 0.25

⇒ Salt in 500 ml of red solution = 500 ml × 10 gpl = 5 g

⇒ Salt in y litres of green solution = y litres × 8 gpl = 8y g 

⇒ Total salt = (5 + 8y) g

⇒ Total volume = 0.5 litres + y litres

⇒ Final concentration = (5 + 8y)/(0.5 + y)

⇒ 9.6 = (5 + 8y)/(0.5 + y)

Cross multiplying

⇒ 4.8 + 9.6y = 5 + 8y

⇒ 1.6y = 0.2

⇒ y = 0.125

∴ x/y = 0.25/0.125 = 2

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