pool : kerosene     3  :  2(initially)     2  :  3(after replacement)     R e m a i n i n g   Q u a n t i t y I n i t i a l   Q u a n t i t y = 1 - R e p l a c e d   Q u a n t i t y T o t a l   Q u a n t i t y   (for petrol)    2 3 = 1 - 10 k  => K = 30  Therefore the total quantity of the mixture in the container is 30 liters.

           Wine                         Water             8L                              32L             1                :               4            20 %                           80% (original ratio)            30 %                           70% (required ratio)   In  ths case, the percentage of water being reduced when the mixture is being replaced with wine.   so the ratio of left quantity to the initial quantity is 7:8   Therefore ,  7 8 = 1 - K 40   => K = 5 Lit

Profit (%) = 9.09 % = 1/11   Since the ratio of water and milk is  1 : 11,   Therefore the ratio of water is to mixture = 1:12   Thus the quantity of water in mixture of 1 liter = 1000 x (1/12) = 83.33 ml

Total no.of boys : no. of girls = 13:27        27             :                13

Total quantity of mixture = 75 litre Milk  :  Water  =  4  :  1                                    3       :       1

By the rule of alligation:Cost of 1 kg rice of 1st kind                  Cost of 1 kg rice of 2nd kind        Required ratio = 60 : 90 = 2 : 3

W 1 : A 1     W 2 : A 2     . . . . .   W N : A N   2 : 3                   4 : 5                    5 : 7    W 1 W 1 + A 1   =   2 5   W 2 W 2 + A 2 = 4 9     W N W N + A N   =   5 12 = 72/180 = 80/180 = 75/180                            =>     5   :   3   Therefore, the ratio is  5: 3

Let quantity of mixture be x liters.   Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid =  x 1 - y x n  units, Where n = no of operations .    So, Quantity of Milk =  x 1 - 6 x 2      Given that, Milk : Water = 9 : 16    => Milk : (Milk + Water) = 9 : (9+16)   => Milk : Mixture = 9 : 25     Therefore,  x 1 - 6 x 2 x = 9 25   => x = 15 liters

Average money received by each = 118/50 = Rs. 2.36 Therefore, Ratio of No.of boys and girls = 56 : 24 = 7 : 3 Therefore, Number of boys = 50 x (7/10) = 35 Number of girls = 50 - 35 = 15

Let the capacity of the pot be 'P' litres.Quantity of milk in the mixture before adding milk = 4/9 (P - 8)After adding milk, quantity of milk in the mixture = 6/11 P.6P/11 - 8 = 4/9(P - 8)10P = 792 - 352 => P = 44. The capacity of the pot is 44 liters.