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A 1-liter solution is 30% acid. One glass of a stronger acid solution is added, producing a mixture that is 40% acid. Three more glasses of the stronger solution are then added, producing a mixture that is 55% acid. Finally, four additional glasses of the stronger solution are added.
If 30 mL of the final mixture is removed, how many milliliters of acid does it contain?
A. 19 mL
B. 20 mL
C. 21 mL
D. 22 mL
E. 24 mL
If 30 mL of the final mixture is removed, how many milliliters of acid does it contain?
A. 19 mL
B. 20 mL
C. 21 mL
D. 22 mL
E. 24 mL
07 Jun 2026, 19:56
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Let the volume of one glass be g liters, and let the stronger solution be x% acid.
Initial solution:
(0.30 + xg)/(1 + g) = 0.40
0.30 + xg = 0.40 + 0.40g
xg = 0.10 + 0.40g ...(1)
After adding 3 more glasses, total added = 4 glasses.
Now:
(0.30 + 4xg)/(1 + 4g) = 0.55
0.30 + 4xg = 0.55 + 2.20g
4xg = 0.25 + 2.20g
Using (1): 4xg = 4(0.10 + 0.40g) = 0.40 + 1.60g
So:
0.40 + 1.60g = 0.25 + 2.20g
0.15 = 0.60g
g = 0.25 L
Substitute into (1):
xg = 0.10 + 0.40(0.25)
= 0.10 + 0.10
= 0.20
x = 0.20/0.25 = 0.80
So the stronger solution is 80% acid.
Now 4 more glasses are added.
Total glasses added = 8.
Final mixture:
If 30 mL is removed, acid removed = (19/30) × 30 = 19 mL.
Answer: A. 19 mL.
Initial solution:
- Volume = 1 L
- Acid = 0.30 L
- Volume = 1 + g
- Acid = 0.30 + xg
(0.30 + xg)/(1 + g) = 0.40
0.30 + xg = 0.40 + 0.40g
xg = 0.10 + 0.40g ...(1)
After adding 3 more glasses, total added = 4 glasses.
Now:
- Volume = 1 + 4g
- Acid = 0.30 + 4xg
(0.30 + 4xg)/(1 + 4g) = 0.55
0.30 + 4xg = 0.55 + 2.20g
4xg = 0.25 + 2.20g
Using (1): 4xg = 4(0.10 + 0.40g) = 0.40 + 1.60g
So:
0.40 + 1.60g = 0.25 + 2.20g
0.15 = 0.60g
g = 0.25 L
Substitute into (1):
xg = 0.10 + 0.40(0.25)
= 0.10 + 0.10
= 0.20
x = 0.20/0.25 = 0.80
So the stronger solution is 80% acid.
Now 4 more glasses are added.
Total glasses added = 8.
Final mixture:
- Volume = 1 + 8(0.25) = 3 L
- Acid = 0.30 + 8(0.25)(0.80)
= 0.30 + 1.60
= 1.90 L
If 30 mL is removed, acid removed = (19/30) × 30 = 19 mL.
Answer: A. 19 mL.
07 Jun 2026, 22:57
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