Eight litres are drawn off from a vessel full of water and substituted by pure milk. Again eight litres of the mixture are drawn off and substituted by pure milk. If the vessel now contains water and milk in the ratio 9:40, find the capacity of the vessel.
Answers
Answer:
14 litres
Step-by-step explanation:
Let the capacity be x
8 litres of water is drawn and replaced with milk
milk = 8 litres
water = (x - 8) litres
Ratio = 8 : (x - 8)
8 litres of the mixture is drawn:
Milk drawn = (8/x)(8) = 64/x
Milk left = 8 - 64/x
8 litres of milk is added:
Milk added = 8 - 64/x + 8 = 16 - 64/x
Find the fraction of milk:
Fraction of milk = [6 - 64/x] ÷ x
Fraction of milk = [16(x - 4)/x] ÷ x
Fraction of milk = 16(x - 4)/x²
Find the fraction of the milk in the final ratio:
Given that the ratio water : milk is 9 : 40
Fraction of milk = 40/(40 + 9) = 40/49
Solve x:
16(x - 4)/x² = 40/49
784(x - 4) = 40x²
784x - 3136 = 40x²
40x² - 784x + 3136 = 0
5x² - 98x + 392 = 0
(x - 14) (5x - 28) = 0
x = 14 or x = 5.6 (rejected, because x is more than 8)
Answer: The capacity of the vessel is 14 litres
Answer:
capacity of container is 14 liter
Step-by-step explanation:
Let x is the capacity of the container.
When 8 litres removed, the volume of liquid inside the container decreases by 8/x.
When 8 litres water removed, remaining amount of water = x-8.
When 8 more litres are removed, the decrease in the water = (8/x)(x-8).
Remaining amount of water = (x-8) - (8/x)(x-8) = (x-8)*(1 - 8/x) = (x-8)*(x-8)/x.
At the end of the process, water:milk = 9:40.
Water constitutes 9 of every 49 liters inside the container, implying that the amount of water = (9/49)x.
(x-8)*(x-8)/x = (9/49)x
(x-8)² = (9/49)x²
x-8 = (3/7)x
7x - 56 = 3x
4x = 56
x = 14