Question

Two vessels contain a mixture of two liquids A and B in the ratio 9:4 and 5:3. In which ratio must liquids be taken from each vessel to give a mixture of the liquid A and B in the ratio 2:1.. Please write all the steps in detail..​

Answer 1

Answer

Answer=Vessel A : Vessel B:: 7:5

Explanation

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