There are two vessels a and b containing mixtures of milk and water in the ratio of 5:x and 8:15 respectively. vessel a contains 48l of mixture. 12l of mixture from vessel a is replaced by 23l mixture of vessel b. final ratio of milk to total mixture in vessel a become 23:59. find the value of x?
Answers
Mixture A :
Ratio of milk to water = 5 : x
When 12 litres are withdrawn we remain with : 48 - 12 = 36 litres
The amount of milk and water is :
Milk = (5 × 36)/(x + 5)
= 180/(x + 5)
Water = (x × 36)/(x + 5)
= 36x/(x +5)
Mixture B:
The ratio of milk to water = 8 : 15
If we withdraw 23 litres and add it to mixture A, the amount of milk and water added is :
Milk = 8/23 × 23 = 8 litres
Water = 15/23 × 23 = 15 litres
We add this to mixture A and get the new amounts of milk and water:
Milk :
180/(x + 5) + 8
Water:
36x/(x + 5) + 15
The total amount of mixture A after the addition is :
23 + 36 = 59 litres
Now the ratio of the amount of milk to the total amount is 23 : 59
Expressing this we have :
{180/(x + 5) + 8} / 59 = 23/59
59{180/(x + 5) + 8} = 23 × 59
10620/(x + 5) + 472 = 1357
10620/(x + 5) = 1357 - 472
10620 / (x + 5) = 885
10620 = 885(x + 5)
10620 = 885x + 4425
10620 - 4425 = 885x
885x = 6195
x = 6195/885
x = 7