Vessel A contains a solution of milk and water in the ratio

Question

Vessel A contains a solution of milk and water in the ratio 1:3. If 8 litres of the mixture is replaced with milk, then the new ratio becomes 3:5. Had p litres of mixture been replaced with milk, the amount of water and milk in the vessel would have become equal. Find the value of p.

A. 9
B. 12
C. 16
D. 20
E. 24

(Source : Wizako)

A. 9
B. 12
C. 16
D. 20
E. 24

(Source : Wizako)

darshakvekaria · Accepted Answer

Quicker way to solve this:

Original ratio: 1:3 or 2:6

Scenario 1:
8 liters of mixed solution replaced with 8 liters of milk
So new ratio = 3:5
From 2:6 to 3:5
Since both the ratios have equal amount of total quantity present, we can say that, 1/8th of water is replaced with equivalent quantity of milk i.e., 1/8, resulting in the ratio 3:5

Scenario 2 says:
If p liters of mix be replaced with milk, new ratio would be 1:1 or 4:4
From 2:6 to 4:4
So 2/8 of water replaced with same quantity of milk.

If 1/8 is 8 liters of, 2/8 is 16 liters.
 Hence, p=16.

harshittahuja · Answer

Vessel A contains a solution of milk and water in the ratio 1:3. If 8 litres of the mixture is replaced with milk, then the new ratio becomes 3:5. Had p litres of mixture been replaced with milk, the amount of water and milk in the vessel would have become equal. Find the value of p.
Solution:
Milk=8x=12
Water=24x=36
Total=32x=48
8 liters of Solution is replaced with milk
so
milk-8x+8-2=8x+6
water=24x-6
(8x+6)/(24x-6)=3/5
40x+30=72x-18
48=32x
actual solution is
Milk =12
water=36
2nd condition
p litres is mixed and replace with milk
milk 12-p/4+p=12+3p/4
water 36-3p/4
12+3p/4=36-3p/4
-24=-6p/4
p=16

Zareensoobuh · Answer

a = 1:3(1+3=4)
we need 8
a = 2:6 (2+6=8)
b=3:5(3+5=8)
2/8+p=3/8-p
16p=1
p=1/16.

ramelan · Answer

can someone pls explain this

Krunaal · Answer

Hi, could you please share any specific part from the above solutions you did not understand / got stuck at, or your working on the problem; that way it would be easier to explain you and address your doubt.

Kinshook · Answer

Vessel A contains a solution of milk and water in the ratio 1:3. If 8 litres of the mixture is replaced with milk, then the new ratio becomes 3:5. Had p litres of mixture been replaced with milk, the amount of water and milk in the vessel would have become equal. Find the value of p.

A. 9
B. 12
C. 16
D. 20
E. 24

(Source : Wizako)

Find the value of p.

Let the volume of solution in the vessel be x litres

Milk = x/4
Water = 3x/4

8 litres of the mixture is replaced with milk
Milk = x/4 - 8*1/4 = x/4 - 2 + 8 = x/4 + 6
Water = 3x/4 - 6
Ratio of milk: water = x/4+6 : 3x/4 - 6 = 3:5
5x/4 + 30 = 9x/4 - 18
x = 48 litres

p litres of mixture been replaced with milk
Milk = x/4 - p*1/4 + p = 48/4 + 3p/4 = 12 + 3p/4
Water = 3x/4 - 3p/4 = 36 - 3p/4
Ratio of milk: water = 12 + 3p/4 : 36 - 3p/4 = 1:1
12 + 3p/4 = 36 - 3p/4
3p/2 = 24
p = 16 litres

IMO C

Ters · Answer

The ratio of milk to water:

\frac{m}{w}  =  \frac{3}{5}

If we add 8 litres of mixture to milk we need to remove 8 litres of mixture from water:

\frac{(x+8)}{(3x-8)}  =  \frac{3}{5}   
5x + 40 = 9x - 24
4x = 64
x = 16

Now we apply same concept for adding p litres of mixture to milk:
 \frac{(x+p)}{(3x-p)}  =  \frac{1}{1}   
x + p = 3x - p
2x = 2p
x = p

Thus it follows that p = 16.

Vessel A contains a solution of milk and water in the ratio

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Vessel A contains a solution of milk and water in the ratio

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