Question

Two same glasses are respectively 1/4th 1/5th full of milk. They are thenfilled
with water and the contents mixed in a tumbler. The ratio of milk and water in
the tumbler is?
A. 3:8
B. 9:31
C. 8:21
D. 10:27

Answer 1

The ratio of milk in the two glasses is

1/4+1/5=9/20

therefore the total ratio of water is

(1-1/4)+(1-1/5)=31/20

so in tumbler the ratio will be

9:31

Answer 2

Answer:  The answer is (B) 9 : 31.

Step-by-step explanation:  Given that there are two glasses which are one-fourth and one-fifth filled with milk. The rest of the two glasses are filled with water and then mixed in a tumbler. We are to find the ratio of milk and water in the tumbler.

The fraction of milk in the first glass is

$M_f=\dfrac{1}{4},$

and the fraction of milk in the second glass is

$M_s=\dfrac{1}{5}.$

Therefore, the fraction of water in the first glass is

$W_f=1-\dfrac{1}{4}=\dfrac{3}{4},$

and fraction of water in the second glass is

$W_s=1-\dfrac{1}{5}=\dfrac{4}{5}.$

So, the total fraction of milk in the tumbler after mixing is

$M=M_f+M_s=\dfrac{1}{4}+\dfrac{1}{5}=\dfrac{9}{20},$

and the total fraction of water is

$W=W_f+W_s=\dfrac{3}{4}+\dfrac{4}{5}=\dfrac{31}{20}.$

Hence, the required ratio is

$\dfrac{9}{20}:\dfrac{31}{20}=9:31.$

Thus, option (B) is correct.