Alligation or Mixture problems
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?
Let the quantity of the wine in the cask originally be x litres. Then, quantity of wine left in cask after 4 operations = [ x ❨ 1 - 8 ❩ 4 ] litres. x ∴ ❨ x(1 - (8/x))4 ❩ = 16 x 81 ⟹ ❨ 1 - 8 ❩ 4 = ❨ 2 ❩ 4 x 3 ⟹ ❨ x - 8 ❩ = 2 x 3 ⟹ 3x - 24 = 2x ⟹ x = 24.
Copper in 4 kg = 4/5 kg and Zinc in 4 kg = 4 x (4/5) kg Copper in 5 kg = 5/6 kg and Zinc in 5 kg = 5 x (5/6) kg Therefore, Copper in mixture = 4 5 + 5 6 = 49 30 kg and Zinc in the mixture = 16 5 + 25 6 = 221 30 kg Therefore the required ratio = 49 : 221
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
EXAMIANS