Alligation or Mixture problems
A beaker contains acid and water in the ratio 1 : x. When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid and water becomes 2 : 5. What is the value of x?
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.
Ratio of milk and water = 2 : 1
Quantity of milk = 60 X 2/3 = 40 litre
Quantity of water = 20 litre
To make ratio, 1: 2, we have to double the water that of milk
So, water should be 80 litre.
That means 80 ? 20 = 60 litre water to be added.
According to figure we can find that the ration would be 1 : 7.Quantity sold at 10% profit = 1 / (1 + 7)× 160 = 20 kgs. Quantity sold at 6% loss = (160 ? 20) = 140 kgs.
Using Alligation rule, (Quantity of cheaper tea) / (Quantity of dearer tea) = (d - m) / (m - c) = 7/3Therefore, they must be mixed in the ratio of 7 : 3.
Milk Water 74% 26% (initially) 76% 24% ( after replacement) Left amount = Initial amount 1 - r e p l a c e d a m o u n t t o t a l a m o u n t 24 = 26 1 - 7 k => k = 91
EXAMIANS