In what proportion must water be mixed with spirit to gain 16 2/3 by selling it at cost price

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Given

Profit gain after mixed water = 14 2/7%

Calculation

Let the cost price of spirit = 1 Rs.

The selling price of the mixture is = 1 Rs.

Mixture selling after gain = 14 2/7%  {Hence 14 2/7% = 100/7}

Cost of mixture is = (100)/(100 + 100/7)× selling price

⇒ {(100)/(700+100)7} × 1  

⇒ (100)/(800/7)

⇒ Cost price of mixture = 700/800

⇒ 7/8

By the rule of alligation, we have:

Raio 1/8 : 7/8

Ratio of water and spirit

1 : 7 

q : p = x : 100  [Here, p = 1 litre and x = 14 2/7]

∴ q : 1 = 14 2/7:100

= 100/7 : 100

Ratio of water and spirit

= 1 : 7

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