Mary needs 30 liters of mocktail consisting of cranberry, apple, and

Question

Mary needs 30 liters of mocktail consisting of cranberry, apple, and grape juice for a party. If each juice must be at least 20% of the resulting cocktail and at the most 80% of the resulting mocktail .

Select for Maximum, the greatest possible quantity of any juice in litres in the mocktail and select for the Minimum, the least possible quantity of any juice in litres in the mocktail. Make only two selections, one in each column.

chetan2u · Accepted Answer

The range given is at least 20% of 30 or 6 litres and at the most 80% or 24.

Max : To maximise one, minimise the other two, so 6 litres each. Therefore max+6+6=30 or max=18

Min : Minimum will be 6 litres itself.

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_blossom_s · Answer

What is the correct answer?

Krunaal · Answer

30 litres of mocktail consists cranberry + apple + grape juice =>  c + a + g =30  ..............(1)

Each  juice should be minimum 20% of whole mocktail => minimum 6 litres (20% of 30 litres)

Now, to find maximum we can substitute minimum value 6 in (1) for 2 juices

6 + 6 + g = 30
g = 18 => this is maximum (it is less than 80% and more than 20%, as per the constraints)

Answer. Maximum = 18 ; Minimum = 6

reyrest · Answer

Shouldn't it be 24 -6 - 6 for the maximum value? because if its 18, the the max percentage of all juices will be 100%? whereas in the question its mentioned as atmost 80% for all 3 combined?

reyrest · Answer

Shouldn't it be 24 -6 - 6 for the maximum value? because if its 18, the the max percentage of all juices will be 100%? whereas in the question its mentioned as atmost 80% for all 3 combined?

Krunaal · Answer

Mary needs total 30 litres of mocktail, and  each juice in that mocktail  should constitute from 20% to 80% of the total 30 litres, thus minimum is 20% of 30 = 6, now to find maximum, we will need to keep two juices at 6 litres, 30 - 6 - 6 = 18 that is the maximum one juice can be. You can try putting a higher value than 18 for one juice, but then you won’t be able to satisfy the minimum condition.

egmat · Answer

The constraint "at most 80%" applies to EACH individual juice, NOT all three combined.

Let's reread the question carefully:

The keyword here is   "each"   - this means:
- Cranberry can be at most  80%  of  30L  =  24L 
- Apple can be at most  80%  of  30L  =  24L 
- Grape can be at most  80%  of  30L  =  24L

Common mistake:   Reading it as "all juices combined must be at most 80%"

Why the maximum is 18, not 24: 
- Total mocktail =  30L 
- To maximize one juice, minimize the others
- Minimum for each juice =  20%  of  30L  =  6L 
-  Therefore:6  +  6  +  ?  =  30 
- Maximum =  18L

Verification: 
- Is  18L  ≥  20%  of  30L ? Yes ( 18  >  6 ) ✓
- Is  18L  ≤  80%  of  30L ? Yes ( 18  <  24 ) ✓
- All three juices add to  100% ? Yes, and that's perfectly fine! ✓

Answer: Maximum = 18L, Minimum = 6L

Remember: All three juices MUST add up to  100%  of the mocktail (since they're the only ingredients). The  80%  limit is for each juice individually, not their sum!

Mary needs 30 liters of mocktail consisting of cranberry, apple, and

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Mary needs 30 liters of mocktail consisting of cranberry, apple, and