Alligation or Mixture problems
Jar A has 36 litres of mixture of milk and water in the respective ratio of 5 : 4. Jar B which had 20 litres of mixture of milk and water, was emptied into jar A, and as a result in jar A, the respective ratio of milk and water becomes 5: 3. What was the quantity of water in jar B?
Jar A has 36 litres of mixture of milk and water in the respective ratio of 5 : 4 => Quantity of milk in Jar A = 5/9 x 36 = 20 litres Quantity of water in Jar A = 36 - 20 = 16 litres Let quantity of water in Jar B = x litres => Quantity of milk in Jar B = (20 - x) litres Acc. to ques, =>[20 + (20-x)]/(16+x) = 5/3 => 120?3x = 80+5x => 5x +3x = 120?80 => 8x = 40 => 5 litres.
Let the price of the mixed variety be Rs. x per kg. By rule of alligation, we have: Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice Rs. 15 Mean Price Rs. x Rs. 20 (20 - x) (x - 15) ∴ (20 - x) = 2 (x - 15) 3 ⟹ 60 - 3x = 2x - 30 ⟹ 5x = 90 ⟹ x = 18.
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.
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.
Customer ratio of Milk and Water is given by Milk :: Water 6.4 0 8 1 + 3 8 = 64 11 64 11 64 10 - 64 11 => Milk : Water = 110 : 11 = 10 : 1 Therefore, the proportionate of Water to Milk for Customer is 1 : 10
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