two vessels contain mixture of milk and water in the ratio 5:2 and 3:1 r

Question

two vessels contain mixture of milk and water in the ratio 5:2 and 3:1 respectively. find the ratio of milk and water in the new solution if two mixtures are mixed in equal amount

answer is 41:15

 

 

 

please explain me in detail

Answer 1

ratios of milk and water are 5:2 and 3:1

5+2=7 and 3+1=4

the LCM of 7 and 4 is 28

5*4=20 units of milk and 2*4=8 units of water

3*7=21 units of milk and 1*7=7 units of water

20+21=41 units of milk and 8+7=15 units of water

the ratio is 41:15

Answer 2

Since we are mixing equal amounts of the two mixtures, let's say we have volume a of each mixture.

We will work our the amount of milk and water in each mixture.

 

First mixture

total volume = a

milk:water ratio = 5:2

sum of ratios = 7

therefore, amount of milk = (5/7)a            eq1

and, amount of water = (2/7)a                 eq2

 

Second mixture
total volume = a
milk:water ratio = 3:1
sum of ratios = 4
therefore, amount of milk = (3/4)a            eq3
and, amount of water = (1/4)a                 eq4

 

After you mix the two mixtures:

For total amount of milk, we add eq1 and eq3

Total amount of milk = (5/7)a + (3/4)a = (41/28)a

Similarly, add eq2 and 4 to get the amount of water in the new mixture

Total amount of water = (2/7)a + (1/4)a = (15/28)a

 

Therefore, the ratio of milk:water in the new mixture = [(41/28)a]/[(15/28)a] = 41/15