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22 Mar 2023, 01:57
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A
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Difficulty:
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Question Stats:
83% (01:54) correct
17%
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A container has 40 gallons of solution that is 10% concentrate and 90% water by volume. How many gallons of concentrate should be added to prepare a solution that is 20% concentrate and 80% water by volume?
(A) 5
(B) 10
(C) 40
(D) 80
(E) 240
Posted from my mobile device
(A) 5
(B) 10
(C) 40
(D) 80
(E) 240
Posted from my mobile device
24 Mar 2023, 07:53
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Given: A container has 40 gallons of solution that is 10% concentrate and 90% water by volume.
Asked: How many gallons of concentrate should be added to prepare a solution that is 20% concentrate and 80% water by volume?
Initial: -
Total = 40 gallons
Concentrate = 10%*40 = 4 gallons
Water = 90%*40 = 36 gallons
Let the gallons of concentrate added be x gallons
Concentrate = 4 + x gallons
Water = 36 gallons
Total = 40 + x gallons
(4+x)/(40+x) = 20%
4 + x = 8 + .2x
.8x = 4
x = 4/.8 = 5 gallons
IMO A
Asked: How many gallons of concentrate should be added to prepare a solution that is 20% concentrate and 80% water by volume?
Initial: -
Total = 40 gallons
Concentrate = 10%*40 = 4 gallons
Water = 90%*40 = 36 gallons
Let the gallons of concentrate added be x gallons
Concentrate = 4 + x gallons
Water = 36 gallons
Total = 40 + x gallons
(4+x)/(40+x) = 20%
4 + x = 8 + .2x
.8x = 4
x = 4/.8 = 5 gallons
IMO A
General Discussion
22 Mar 2023, 02:13
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Sol. Initial Ratio of C and W = 1 : 9 = 4 : 36
Final ratio of C and W = 1 : 4 = 9 : 36
Since amount of water is unchanged, change in ratio is due to the change in concentrate only which is 9 – 4 = 5 unit ratio,
Initial ratio is 4 + 36 = 40 unit ratio which is equivalent to the 40 gallons. Hence value of 5 unit ratio will be equivalent to 5 gallons of concentrate.
Hence Correct Answer is A.
Final ratio of C and W = 1 : 4 = 9 : 36
Since amount of water is unchanged, change in ratio is due to the change in concentrate only which is 9 – 4 = 5 unit ratio,
Initial ratio is 4 + 36 = 40 unit ratio which is equivalent to the 40 gallons. Hence value of 5 unit ratio will be equivalent to 5 gallons of concentrate.
Hence Correct Answer is A.
