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A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid P was contained in the container initially?
- a)23
- b)21
- c)19
- d)17
Correct answer is option 'B'. Can you explain this answer?
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A container contains a mixture of two liquids P and Q in the ratio 7 :...
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A container contains a mixture of two liquids P and Q in the ratio 7 :...
Let initial quantity of liquid P be = 7x
let initial quantity of liquid Q be = 5x
when 9 lts. of liquid is drawn off from both liquids
P = 9 x 7\12 = 21\4
Q = 9 x 5\12 = 15\4
Remaining liquids, P= 7x-21\4 and Q = 5x-15\4
since liquid Q has been mixed=> 5x-15\4+9 = 5x=21\4
given ratio of P:Q= 7:9
(7x-21\4):(5x+21\4) = 7:9
9(7x-21\4)=7(5x+21\4)
63x - 21X9\4 = 35x +21X7\4
63x-35x = 147\4+189\4
28x = 336\4
x = 336\4 X1\28
x = 3
therefore,initial quantity of liquid P = 7x i.e. 21 lts.
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A container contains a mixture of two liquids P and Q in the ratio 7 :...
Given:
- The initial ratio of liquids P and Q in the container = 7:5
- 9 litres of mixture are drawn off
- The container is filled with Q
- The new ratio of P and Q becomes 7:9
To find: How many litres of liquid P was contained in the container initially?
Solution:
Let's assume that the container initially contains 7x and 5x liters of liquids P and Q respectively.
Step 1: Calculation of initial quantity
- Initial ratio of P and Q = 7:5
- Let the common ratio be k
- So, we can write 7x = 7k and 5x = 5k
- Simplifying, we get x = k
Therefore, the container initially contains 7k and 5k liters of liquids P and Q respectively.
Step 2: Calculation of quantity after drawing mixture
- 9 litres of mixture are drawn off from the container which contains a total of 7k+5k = 12k liters of liquid
- Therefore, the remaining liquid in the container = 12k - 9 = 3k liters
- Let the quantity of liquid Q that is added to the container be q
- So, the container now contains 3k + q liters of liquid Q and 7k liters of liquid P
Step 3: Calculation of new ratio
- According to the question, the new ratio of P and Q becomes 7:9
- So, we can write (7k)/(3k+q) = 7/9
- Simplifying, we get q = 10k/3
Step 4: Calculation of initial quantity of P
- We know that the initial quantity of liquid P in the container is 7k liters
- From step 2, we know that the container now contains 3k + q liters of liquid Q and 7k liters of liquid P
- Substituting the value of q from step 3, we get the total quantity of liquid in the container as (3k+10k/3) + 7k = 20k/3
- But we also know that 9 liters of mixture were drawn off from the container
- So, the initial quantity of liquid in the container = (20k/3) + 9 liters
- Equating this to the initial quantity of liquid P (7k liters), we get:
(20k/3) + 9 = 7k
- Simplifying, we get k = 3
- Therefore, the initial quantity of liquid P in the container = 7k = 7*3 = 21 liters
Therefore, the correct answer is option B (21 liters).
- The initial ratio of liquids P and Q in the container = 7:5
- 9 litres of mixture are drawn off
- The container is filled with Q
- The new ratio of P and Q becomes 7:9
To find: How many litres of liquid P was contained in the container initially?
Solution:
Let's assume that the container initially contains 7x and 5x liters of liquids P and Q respectively.
Step 1: Calculation of initial quantity
- Initial ratio of P and Q = 7:5
- Let the common ratio be k
- So, we can write 7x = 7k and 5x = 5k
- Simplifying, we get x = k
Therefore, the container initially contains 7k and 5k liters of liquids P and Q respectively.
Step 2: Calculation of quantity after drawing mixture
- 9 litres of mixture are drawn off from the container which contains a total of 7k+5k = 12k liters of liquid
- Therefore, the remaining liquid in the container = 12k - 9 = 3k liters
- Let the quantity of liquid Q that is added to the container be q
- So, the container now contains 3k + q liters of liquid Q and 7k liters of liquid P
Step 3: Calculation of new ratio
- According to the question, the new ratio of P and Q becomes 7:9
- So, we can write (7k)/(3k+q) = 7/9
- Simplifying, we get q = 10k/3
Step 4: Calculation of initial quantity of P
- We know that the initial quantity of liquid P in the container is 7k liters
- From step 2, we know that the container now contains 3k + q liters of liquid Q and 7k liters of liquid P
- Substituting the value of q from step 3, we get the total quantity of liquid in the container as (3k+10k/3) + 7k = 20k/3
- But we also know that 9 liters of mixture were drawn off from the container
- So, the initial quantity of liquid in the container = (20k/3) + 9 liters
- Equating this to the initial quantity of liquid P (7k liters), we get:
(20k/3) + 9 = 7k
- Simplifying, we get k = 3
- Therefore, the initial quantity of liquid P in the container = 7k = 7*3 = 21 liters
Therefore, the correct answer is option B (21 liters).
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A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid P was contained in the container initially?
a)23b)21c)19d)17Correct answer is option 'B'. Can you explain this answer?
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Solutions for A container contains a mixture of two liquids P and Q in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with Q, the ratio of P and Q becomes 7 : 9. How many litres of liquid P was contained in the container initially?
a)23b)21c)19d)17Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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