Question

three glasses A B and C with their capacities in the ratio 2:3:4 are filled with a mixture of spirit and water. the ratio of spirit to water in a,b and c is 1:5, 3:5, 5:7 respectively. if the contents of this glasses are mixed together find the ratio of spirit to water in the mixture​

Answer 1

If the contents of these three glasses A, B & C are mixed together then the ratio of spirit to water in the mixture is 25:47.

Step-by-step explanation:

Step 1:

The capacities of the three glasses A, B & C are in the ratio = 2:3:4

Let’s assume the capacities each glasses in terms of litres i.e.,  

Capacity of A = 2 litres

Capacity of B = 3 litres  

Capacity of C = 4 litres  

Now,

The quantity of spirit and water in each of the glasses are as follows:

Glass A :

Ratio of spirit to water = 1:5

So,  

Quantity of spirit = $\frac{1}{1+5}$ * 2 = $\frac{2}{6}$

Quantity of water = $\frac{5}{6}$ * 2 = $\frac{10}{6}$ = $\frac{5}{3}$

Glass B:

Ratio of spirit to water = 3:5

So,  

Quantity of spirit = $\frac{3}{3+5}$ * 3 = $\frac{9}{8}$

Quantity of water = $\frac{5}{8}$ * 3 = $\frac{15}{8}$

Glass C:

Ratio of spirit to water = 5:7

So,  

Quantity of spirit = $\frac{5}{5+7}$ * 4 = $\frac{20}{12}$ = $\frac{5}{3}$

Quantity of water = $\frac{7}{12}$ * 4 = $\frac{28}{12}$ = $\frac{7}{3}$

Step 2:

Since the contents of all the 3 glasses are mixed together, so we will add the quantities of spirit and water in each of glasses separately in order to get the final ratio of spirit to water in the mixture.

Therefore,

The total quantity of spirit in the mixture = $\frac{1}{3}$ + $\frac{9}{8}$ +$\frac{5}{3}$ = $\frac{8+27+40}{24}$ = $\frac{75}{24}$

And,

The total quantity of water in the mixture = $\frac{5}{3}$ + $\frac{15}{8}$ + $\frac{7}{3}$ = $\frac{40+45+56}{24}$ = $\frac{141}{24}$

Thus,  

The ratio of spirit to water in the mixture is given as,

= $\frac{\frac{75}{24}}{\frac{141}{24}}$

= $\frac{75}{141}$

= $\frac{25}{47}$ or 25:47

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Answer 2

Answer:

Step-by-step explanation: