Two vessels X and Y of capacities one and two litres respectively are completely filled with mixtures of two chemicals A and B. The ratio by volume of the chemicals A and B in X and Y are 3:2 and 4:5 respectively. The contents of A and B are mixed and the combination is kept in a vessel C of capacity of four litres. How many litres of Chemical A should be added to the combination so as to make the ratio of A to B equal to 1:1?
Answers
Answer=Vessel A : Vessel B:: 7:5
Ratios are 4:3 (4+3=7) and 2:3 (2+3=5). So LCM of 7, 5 is 35.
Now, for 35 liter mix.
Let M=milk,W=water
Vessel A,
M:W= 4:3 (4+3=7) means in 35 liter mix. Milk is 4*35/7=20 liter and water is 3×35/7=15 liter.
Vessel B,
M:W=2:3(2+3=5) means in 35 liter mix. Milk is 2×35/5=14 liter and water is 3×35/5=21 liter.
For Vessel C,
M:W=1:1(required)
Let ratio of Vessel A=x and Vessel B=y.
In Vessel C , both milk and water will be in equal quantity. So,
Net quantity of milk= Net quantity of water
20x+14y=15x+21y
5x=7y
x/y=7/5
So, x:y=7 :5
Vessel A : Vessel B:: 7:5
Answer check-
Vessel A, milk=20×1.4=28 liter,water=15×1.4=21 liter and net quantity=28+21=49 liter
Vessel B , milk=14 liter, water=21 liter and net quantity=35 liter
Afrer Mixing both Vessels,
Net quantity=49+35=84 liter
Milk=28+14=42 liter
Water=21+21=42 liter
Answer:
1/135
Step-by-step explanation:
Amount of chemical A in container C = (3/5) +(4/9) *2 [Since 2litre in Y]
=67/45 l
Amount of chemical B in container C = (2/5) +(5/9) *2
=68/45 l
Ratio of chemicals A and B in container C=67:68
Amount of A to be added=68/ (67+68)- 67/ (67+68)
=1/135