Q. A vessel contains milk and water in the ratio 3:5. When 6 litres of this solution is
removed and replaced with water, the ratio of milk and water becomes 5:9. How many
litres of the solution was present in the vessel originally?
Answers
Given : A vessel contains milk and water in the ratio 3:5. When 6 litres of this solution is removed and replaced with water, the ratio of milk and water becomes 5:9.
To Find : How many litres of the solution was present in the vessel originally?
Solution:
Let say Solution present originally = 8k litres
Milk = 3k
water = 5k
When 6 litres of this solution is removed and replaced with water
milk remains = 3k - (3k/8k)6 = 3k - 9/4 litre = (12k - 9)/4 litre
and water = 5k - (5k/8k)6 + 6 = 5k + 9/4 litre = (20k + 9)/4 litre
ratio of milk and water becomes 5:9.
=> (12k - 9)/4 : (20k + 9)/4 = 5 : 9
=> 12k - 9 : 20k + 9 = 5 : 9
=> (12 k - 9)/(20 k + 9) = 5/9
=> 9 (12k - 9) = 5(20k + 9)
=> 108k - 81 = 100k + 45
=> 8k = 126
Solution present originally = 8k litres
= 126 litres
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Solution :-
we know that,
- FC = IC(1 - x/V) .
- FC = final concentration .
- IC = initial concentration .
- x = Quantity removed / added.
- V = Total volume. .
given that,
→ Milk : water = 3 : 5 .
→ Milk = (3/8) = IC .
in final ,
→ Milk = 5 : 9 = (5/14) = FC .
then,
→ (5/14) = (3/8)[1 - (6/V)]
→ (5/14) * (8/3) = 1 - (6/V)
→ (20/21) = 1 - (6/V)
→ 6/V = 1 - (20/21)
→ 6 / V = (1/21)
→ V = 126 Litres. (Ans.)
Hence, 126 Litres of the solution was present in the vessel originally .
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