Alligation or Mixture problems
The average age of 6 members of a family is 20 years. If the age of the servant is included, then the average age increase by 25%. What is the age (in years) of the servant?
Ratio of milk and water = 2 : 1Quantity of milk = 60 X 2/3 = 40 litreQuantity of water = 20 litreTo make ratio, 1: 2, we have to double the water that of milkSo, water should be 80 litre.That means 80 ? 20 = 60 litre water to be added.
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 x 4 litres ? x 1 - 8 x 4 x = 16 81 ? 1 - 8 x 4 = 2 3 4 ? x = 24
By the rule of alligation: C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.
Given rate of wheat at cheap = Rs. 2.90/kg Rate of wheat at cost = Rs. 3.20/kg Mixture rate = Rs. 3/kg Ratio of mixture = 2.90 3.20 3 (3.20 - 3 = 0.20) (3 - 2.90 = 0.10) 0.20 : 0.10 = 2:1 Hence, wheat at Rs. 3.20/kg be mixed with wheat at Rs. 2.90/kg in the ratio of 2:1, so that the mixture be worth Rs. 3/kg.
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