A tricky ratio problem?

Question

Two containers hold identical quantities of diluted fruit juice. In one container the ratio of juice to water is 2:5. In the other, the ratio of juice to water is 3:7. If both lots of diluted fruit juice were tipped into one single container, what would the ratio of juice to water be?

Answer 1

The answer is 41:99

because...

2:5 implies division into 7 parts in total
3:7 implies 10 parts

7 & 10 both go into 70, so re-write the ratios so that they go into 70.

2:5 = 20:50 (multiplying by 10:10)
3:7= 21:49 (multiplying by 7:7)

We now have ratios that both suggest equal quantities, i.e. 70 parts, of liquid in total.

Adding the respective parts of juice (20+21) and water (50+49),
we get a ratio of juice:water = 41:99.

Answer 2

Let the identically sized containers be L

first container contains 2/7 x L juice
and 5/7 x L of water

Second container contains 3/10 x L juice
and 7/10 x L of water

Total of water in use = 5/7 x L + 7/10 x L

= [{50 + 49}/70] x L
= 99/70 x L
= 1.414 x L


Total of juice = 2/7 x L + 3/10 x L

=[{20 + 21}/70] x L
= 41/70 x L
= 0.585 x L

Add Juice amount to Water amount

[0.585 x L] + [1.414 x L] = 2L

Hence the 2 containers of capacity 'L' each - we started with :-)


Combined Amounts Ratio

Juice to Water
41 : 99

Answer 3

In the first container, the portion of juice is 2/7 and the portion of water in it is 5/7.(i.e. if the whole container is divided into seven parts, water will constitute 2 parts and juice will constitute 5 parts). Similarly, the other container which has the same volume(quantity) of the mixture, will have 3/10 and 7/10 of juice and water respectively. Now if both the mixtures are added, the resulting volume will become(2/7 + 3/10) of juice and (5/7+7/10) of water. Except for the fact that the new volume doubles, the ratio of juice and water never matters. Here I assume that the juice is like ethyl alcohol and water is just distilled water and they dissolve. Thus 41:99 is the answer.

Answer 4

Ensure that the total number of parts is the same for both containers.

1st container => 2:5 (multiplied by 10) => 20:50
2nd container => 3:7 (multiplied by 7) => 21:49

New ratio => 20+21 : 50+49 = 41:99

Answer 5

Juice:
(2/7 * ½) + (3/10 * ½) = 2/14 + 3/20 = (20 + 21)/ 140 = 41/140

Water:
(5/7 * ½) + (7/10 * ½) = 5/14 + 7/20 = (50 + 49)/ 140 = 99/140

New ratio:
Juice : Water
41/140 : 99/140
41 : 99

Answer 6

both containers have same quantities of diluted fruit juice
1st containers fruit:water ratio=2:5
therefore say it has total of 7 liter fruit juice,then 2 liter is juice & 5 liter is water.
2nd container fruit:water ratio=3:7
therefore say it has total of 10 liter fruit juice,then 3 liter is juice & 7 liter is water.
the largest common of 7 & 10 is 70.
therefore if both container have 70 liter of diluted fruit juice
1st container has 20 liter fruit juice:50 liter water
2nd container has 21 liter fruit juice:49 liter water
total would be 41 liter fruit juice:99 liter water
therefore the ratio would be 41:99

Answer 7

Container 1
Volume X
(2/7) X is juice

Container 2
Volume X
(3/10).X is juice

Volume when mixed = 2X

Volume of juice = (2/7).x + (3/10).x
Volume of juice = (20/70).x + (21/70).x
Volume of juice = (41 / 70).x

Volume of water = 2x - (41/70).x = (99/70).x

Ratio of juice:water = 41 : 99

Answer 8

Since both containers have the same amount of total liquid, that makes our life easier

Container 1:
2/7 juice
5/7 water

Container 2:
3/10 juice
7/10 water

Combined
41/70 juice
99/70 water

juice:water = 41:99

Answer 9

Let the containers contain x litres of diluted juice
In the first container,
quantity of juice=2x/7,and
quantity of water=5x/7
In the second container,
quantity of juice=3x/10
quantity of water=7x/10
Therefore,when mixed,
total qty.of juice
=2x/7 + 3x/10
=41x/70 litres
Total quantity of water
=5x/7 +7x/10
=99x/70 litres
Hence the new ratio of juice and water would be
41x/70:99x/70
=41:99 ans.

Answer 10

Let the answer be a : b

2 : 5 = 2/7 : 5/7 and 3 : 7 = 3/10 : 7/10

a / (a + b) = 2/7 + 3/10 = 41 / 70................................ 1
b / (a + b) = 5/7 + 7/10 = 99 / 70................................ 2

so dividing 1 by 2 ...........a : b = 41 : 90