ahahkhyati.j wrote:A can contains a mixture of two liquids A and B in ratio of 7:5. 9 liters of mixture is drawn off and the can is filled with B. The new ratio is 7:9. How many liters of A was there in the can initially?
A. 25
B. 21
C. 20
D. 10
E. 14
An alternate approach is to PLUG IN THE ANSWERS, which represent the original volume of A.
Since original
A:B =
7:5, the original volume of A is likely to be a MULTIPLE OF 7.
Implication:
The correct answer choice is probably B or E.
Since new A:B = 7:9, and 7+9=16, (new A)/(total volume) = 7/16.
Implication:
After 9 liters are removed from the can and replaced with pure B, the remaining volume of A must constitute 7/16 of the total volume.
Answer choice B: 21
Since original A:B = 7:5 = 21:15, original A = 21 liters and original B = 15 liters, for a total of 36 liters.
When 9 of the 36 liters are removed, since 9/36 = 1/4, A's volume and B's volume are each reduced by 1/4.
Thus:
Remaining A = (3/4)(21) = 63/4.
(remaining A)/(total volume) = (63/4)/36 = 7/16.
Success!
The correct answer is
B.
Answer choice E: 14
Since original A:B = 7:5 = 14:10, original A = 14 liters and original B = 10 liters, for a total of 24 liters.
When 9 of the 24 liters are removed, since 9/24 = 3/8, A's volume and B's volume are each reduced by 3/8.
Thus:
Remaining A = (5/8)(14) = 35/4.
(remaining A)/(total volume) = (35/4)/24 ≠7/16.
Eliminate E.
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