Prepare 2L of solution of 60% alcohol from 40% alcohol and 90% alcohol. How many mal will be taken from each strength?

Answer 1

You can use alligation: (if not familiar, look it up)

Have.......Want......Need.....

40%..........................30.........

................60%..................

90%..........................20.......

You need 30 parts of the 40% and 20 parts of the 90%. This adds to 50 parts which we set to 2 L. Thus, each part represents 2 L/50 = 0.04 L/part = 40 mls.

So, 30 parts x 40 mls/part = 1200 mls of 40%

20 parts of 40 mls/part = 800 mls of 90%

Done with algebra:

(x ml)(40) + (2000 - x ml)(90) = 2000 ml x 60

40x + 180,000 - 90x = 120,000

50x = 60,000

x = 1200 mls of 40% leaving the rest (800 ml) of 90%

Answer 2

You will need to use Alligation Method.

1. Convert 2 L to 2,000 ml
2. Subtract the desired strength from the 2 available strengths. The resulting number are called "parts". (Don't worry about - or + signs here)
3. 90% - 60% = 30 parts and 40% - 60% = 20 parts
4. Add the 2 parts to get the total number of parts: 30 + 20 = 50 parts
5. Divide the volume by the total parts: 2,000 ml/ 50 parts = 40 ml/ 1 part .This give you a ratio.
6. Multiply this ratio with the parts calculated from step 2 to find the volume required from each strength.
7. 40 ml/ 1 part x 30 parts = 1200 ml of 90% strength
8. 40 ml/ 1 part x 20 parts = 800 ml of 40% strength
9. You can double check your answer by adding all of the volumes together to see if it equals the total volume.
10. 1,200 ml + 800 ml = 2,000 ml Since the total volume calculated matches the volume we were given, it reassures us that we made the correct calculations.