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 9 of 10.
Prabhas said:
9 years ago
Assume 7 : 5 as 12 liters.
9 liters are drawn form the mixture.
So,
12 - 9 = 3.
Then,
7 * 3 = 21 and 5 * 3 = 15.
9 liters are drawn form the mixture.
So,
12 - 9 = 3.
Then,
7 * 3 = 21 and 5 * 3 = 15.
Rahul said:
9 years ago
Can we solve this problem with the formula of adulteration?
Simhachalam said:
9 years ago
@Anil Kumar Jat.
Your method is the easiest way to solve the problem. Thank you very much.
Your method is the easiest way to solve the problem. Thank you very much.
Priyanka kumari said:
9 years ago
Please, can anyone explain it in short term?
Bony said:
9 years ago
We have two ratios 7:5 and 7:9, let's make it to 28:20 and 21:27 took LCM of their sum to make the total equal).
On drawing 9 litres, 7/12 * 9 = 21/4 amount of A is lost.
This 21/4 corresponds to a change of 7 units in the ratio (28 : 27, 28 : 20).
So 1 unit in the ratio corresponds to 21/(4 * 7) = 3/4.
Initial amount of A corresponds to 28 units (28:20) is our ratio, so 28 units = 28 * 3/4 = 21 litres.
No difficult equations involved. Just make sure that the sum of the ratios in initial and final cases remain the same.
On drawing 9 litres, 7/12 * 9 = 21/4 amount of A is lost.
This 21/4 corresponds to a change of 7 units in the ratio (28 : 27, 28 : 20).
So 1 unit in the ratio corresponds to 21/(4 * 7) = 3/4.
Initial amount of A corresponds to 28 units (28:20) is our ratio, so 28 units = 28 * 3/4 = 21 litres.
No difficult equations involved. Just make sure that the sum of the ratios in initial and final cases remain the same.
SURAJ said:
9 years ago
Here is the simplest method I'm going to discuss.
Since we are not adding anything in A.
Therefore.
After mixing A =7/(7 + 9) = 7/16.
7/16 = 7/12 (volume before replacement/volume after replacement).
7/16 = 7/12 ((12x - 9)/(12x - 9 + 9)).
Then, x = 6.
Then finally we get 21L.
Since we are not adding anything in A.
Therefore.
After mixing A =7/(7 + 9) = 7/16.
7/16 = 7/12 (volume before replacement/volume after replacement).
7/16 = 7/12 ((12x - 9)/(12x - 9 + 9)).
Then, x = 6.
Then finally we get 21L.
Kiran said:
10 years ago
Hi.
Can you explain me why we take 7/12 and 5/12?
Can you explain me why we take 7/12 and 5/12?
Deepthi said:
10 years ago
Can any one explain it again please?
Gopika S S said:
9 years ago
Thanks @Srividhya, your explanation is much better.
Siddhesh said:
10 years ago
Can any one tell me how we calculate (5x-15/4)+9?
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