Question

What would be the ratio of milk and water in a final mixture formed by mixing milk and water that are present in three vessels of capacity 1l, 2l, and 3l respectively and in the ratios 5:1, 3:2 and 4:3 respectively?
31.4326388888889
33.6666666666667
33.1201388888889
31.4534722222222

Answer 1

Given:

The three vessels contains mixture of water and milk  in ratio as follows

1L  -     5:1

2L -     3:2

3L -     4:3

To find:

We have to find the ratio of milk and water after mixing the three vessels

Solution:

Consider vessel 1 having 1L mixture, the ratio of  milk:water = 5:1

Amount of milk in 1L vessel = $\frac{5}{6}(1)$ = $\frac{5}{6}L$

Amount of water in 1L vessel = $\frac{1}{6}(1)$ = $\frac{1}{6}L$

Consider vessel 2 having 2L mixture,the ratio of milk:water = 3:2

Amount of milk in 2L vessel = $\frac{3}{5}(2)$ = $\frac{6}{5}L$

Amount of water in 2L vessel = $\frac{2}{5}(2)$ = $\frac{4}{5}L$

Consider vessel 3 having 3L mixture,the ratio of milk:water = 4:3

Amount of milk in 3L vessel = $\frac{4}{7}(3)$ = $\frac{12}{7}L$

Amount of water in 3L vessel = $\frac{3}{7} (3)$ = $\frac{9}{7} L$

Now total amount of milk=Amount of milk in (vessel1+vessel2+vessel3)

                                         =   $\frac{5}{6}L$ +  $\frac{6}{5}L$ +  $\frac{12}{7}L$

                                         = $\frac{175+252+360}{210}$

Total amount of milk        = $\frac{787}{210}$

Now total amount of water=Amount of water in(vessel1+vessel2+vessel3)

                                            =  $\frac{1}{6}L$ +  $\frac{4}{5}L$ +  $\frac{9}{7} L$

                                            = $\frac{35+168+270}{210}$

Total amount of water        = $\frac{473}{210}$

Now milk:water =  $\frac{787}{210}$ :  $\frac{473}{210}$ = 1.66384