A vessel contains milk and water in the ratio 3 : 2. The volume of the contents is increased by 50% by adding water to it. From this resultant solution 30 L is withdrawn and then replaced with water. The resultant ratio of milk water in the final solution is 3 : 7. Find the original volume of the solution.
A. 80 L
B. 65 L
C. 75 L
D. 82 L
Answer: Option A
Solution(By Examveda Team)
Let the original volume be x. then, quantity of milk and water, = $$\frac{{3x}}{5}$$ and $$\frac{{2x}}{5}$$ respectively. After adding water to it, the volume becomes 150%, the quantity of milk and water, = $$\frac{{3x}}{5}$$ and $$\frac{{9x}}{10}$$ $$\frac{{\frac{{3x}}{5} - 12}}{{\frac{{9x}}{{10}} + 12}} = \frac{3}{7}$$ 14(3x - 60) = 3(9x + 120) Or, x = 80 LThis Question Belongs to Arithmetic Ability >> Alligation
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Comments ( 9 )
Related Questions on Alligation
A. $$\frac{{1}}{{2}}$$ kg
B. $$\frac{{1}}{{8}}$$ kg
C. $$\frac{{3}}{{14}}$$ kg
D. $$\frac{{7}}{{9}}$$ kg
A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres
Let,The Quantity of Milk is 3x;
The Quantity of Water is 2x;
Total Quantity of mixure is 5x
New Quantity of Milk is 3x;
New Quantity of Water is 3x+5X50%=4.5x;
New Ratio Milk to Water=3x:4.5x=2:3;
ATQ,
3x-30X2/5:4.5x-30X3/5+30=3:7;
or,3x-30X2/5:4.5x-30X3/5+30=3:7;
3. 2=5
Now 7.5
3. 4.5
2. 3
3. 7
6. 9
6. 14
5=30
15=90
90+30=120
120/150 100=80
∆:
3/5.================1
=========7/10=======
3:1
1/4=30
1--120
7.5=120
5=16
1=80
One more by alligation
2/5 0
3/10
3/10 1/10
3 1
1/4=30 total 120
7 .5=120
5=80
Ye sirf ratio method hai
3 2
+2.5
3 4.5
2 3
3 7 make milk equl
6 9
6 14
5/20=1/4 replced
1/4=30
120
7.5 =120
5=80
3:2
+2.5
3:4.5
3x-12/4.5x-18+30=3/7
21x-84=13.5x+36
7.5x=120
X=16
5x=80
thanks a lot !!:)
Let there be 5x of solution to begin with, 3x milk, 2x water.
Now, we add 50% water, Solution becomes 7.5x containing 3x milk and 4.5x water.
30L is withdrawn and replaced with water. Milk and water are in ratio 3:4.5 ie. 2:3 presently. This means out of this 30L withdrawn, These is 2 parts milk and 3 parts water. 12L Milk and 18 L water.
Basically 12L milk is replaced with water. Final equation becomes :
(3x-12)/(4.5x+12) = 3/7.
Now solve for x, Which comes out to be 16.
Original volume was 5x= 5*16 = 80L
please explain how is it 3x-12/9x+12