Two vessels A and B contains milk and water in the ratio of 8 : 5 and 5 : 2, respectively.  The ratio in which these two be mixed to get a new mixture containing 69\(\frac{3}{13}\) % milk is?

2 : 7

*[23\(\frac{1}{13}\) % = \(\frac{3}{13}\)]*
therefore, [69\(\frac{3}{13}\) % = \(\frac{9}{13}\)] 

 [\(\frac{Milk}{Water}\)  = \(\frac{9}{4}\)]

              Milk         Water         Total

     I  →     8      :       5       →    13   (×7              

    II  →     5      :       2       →     7    (×13             

                9      :       4       →    13    (×7   ←  (Required ratio)

Make total quantity equal.

Use Alligation method on milk only

Therefore, mixtures should be mixed in the ratio 2: 7