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The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained? 

The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?  Correct Answer 3 : 5

Let x litre of the first mixture and y litre of the second mixture are mixed.

Quantity of spirit in x litre of the first mixture = 5x/6

Quantity of spirit in y litre of second mixture = 3y/10

The total quantity of the resultant mixture = (x + y)

Quantity of spirit in (x + y) litre of the resultant mixture = (x + y) /2

5x/6 + 3y/10 = (x + y) /2

⇒ (25x + 9y) /30 = (x + y) /2

⇒ 25x + 9y = 15 × (x + y)

⇒ 25x + 9y = 15x + 15y

⇒ 10x = 6y

⇒ x/y = 3/5

∴ required ratio = 3 : 5

Alternative method :

Concentration of spirit in the first mixture = 5/6

Concentration of spirit in the second mixture = 3/10

Concentration of spirit in the resultant mixture = 1/2

By rule of allegation,

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∴ Required ratio = (1/5) : (1/3) = 3 : 5

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