Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 3)
3.
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Answer: Option
Explanation:
Suppose the can initially contains 7x and 5x of mixtures A and B respectively.
| Quantity of A in mixture left = |  |
7x - | 7 | x 9 |  |
litres = | |
7x - | 21 | litres. |
| 12 | 4 |
| Quantity of B in mixture left = | |
5x - | 5 | x 9 | |
litres = | |
5x - | 15 | litres. |
| 12 | 4 |
 |
|
= | 7 | |||||
|
9 |
 |
28x - 21 | = | 7 |
| 20x + 21 | 9 |
252x - 189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21 litres of A.
Discussion:
100 comments Page 4 of 10.
Ricky said:
1 decade ago
Even after drawing off some mixture, the mixture remains in the same ratio which is 7:5.
Now it 7x/(5x+9) =7/9 i.e. x=9/4.
Quantity of liquid A in the remaining mixture = 7X9/4 = 63/4.
And quantity of A in the drawn off mixture = (9/12)X7 = 63/12.
Total quantity is (63/4)+63/12 = 21 answer :).
Now it 7x/(5x+9) =7/9 i.e. x=9/4.
Quantity of liquid A in the remaining mixture = 7X9/4 = 63/4.
And quantity of A in the drawn off mixture = (9/12)X7 = 63/12.
Total quantity is (63/4)+63/12 = 21 answer :).
Jumcy said:
1 decade ago
See the ratio of A = 7, check the options which are divisible by 7, 21 is there, simple tricky way.
Sumanth said:
1 decade ago
Most easy answer.
Check options for given ratio of 7:5. Only option is 21.
Check it if a is 21 then b=15.
a:b = 21:15.
Now take 9 liters from 21 i.e. 21-9=12 now add it to 15 becomes 27.
But after taking also ratio is 7:9. So answer is 21.
Check options for given ratio of 7:5. Only option is 21.
Check it if a is 21 then b=15.
a:b = 21:15.
Now take 9 liters from 21 i.e. 21-9=12 now add it to 15 becomes 27.
But after taking also ratio is 7:9. So answer is 21.
Renu said:
1 decade ago
Hi Vaishali can you please explain.
Dipika said:
10 years ago
Fraction of B in original mixture = 5/12 [A:B = 7:5 so B = 5/12].
Fraction of B in resultant mixture = 9/16 [A:B = 7:9 so B = 9/16].
Fraction of B in second mixture = 1 [replacement is made by B so B is 100%].
Applying the rule of allegation.
9/16-5/12 = 7/48.
1-9/16 = 7/16.
Therefore, ratio is 3:1.
Hence amount of liquid transferred was [(3*9)+(1*9)] = 36.
So amount of A = 7/12*36 = 21.
Fraction of B in resultant mixture = 9/16 [A:B = 7:9 so B = 9/16].
Fraction of B in second mixture = 1 [replacement is made by B so B is 100%].
Applying the rule of allegation.
9/16-5/12 = 7/48.
1-9/16 = 7/16.
Therefore, ratio is 3:1.
Hence amount of liquid transferred was [(3*9)+(1*9)] = 36.
So amount of A = 7/12*36 = 21.
Priya said:
10 years ago
I don't understand can you people explain me much better?
Priya said:
10 years ago
I don't understand can you people explain me much better?
Siddhesh said:
10 years ago
Can any one tell me how we calculate (5x-15/4)+9?
Ramakrishana said:
10 years ago
Just divide the 9 liters 7:5.
That is 21/4 and 15/4. They are 7x, 5x.
Then subtracted from their ratios.
That is 7x-21/4, 15x-15/4 then B is added to the mixture.
That is 15x-15/4+9.
((7x-21/4)):(5x-15/4+9) = 7:9.
You will get x = 3 then 7x = 21.
That is 21/4 and 15/4. They are 7x, 5x.
Then subtracted from their ratios.
That is 7x-21/4, 15x-15/4 then B is added to the mixture.
That is 15x-15/4+9.
((7x-21/4)):(5x-15/4+9) = 7:9.
You will get x = 3 then 7x = 21.
(1)
Ramakrishna said:
10 years ago
= (5x*4-15+9*4)/4.
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