Question

A vessel contains liquid a and b in ratio 5:3. if 16 litres of the mixture are removed and the same quantity of liquid b is added,the ratio becomes 3:5.what quantity does the vessel hold?

Answer 1

8:5 quantity does the vessel hold.

Answer 2

Answer:

Total quantity the vessel hold =40 L

Step-by-step explanation:

Given : A vessel contains liquid a and b in ratio 5:3. if 16 litres of the mixture are removed and the same quantity of liquid b is added,the ratio becomes 3:5.

To find : What quantity does the vessel hold?

Solution :

Let the quantity of liquid P and Q be 5x and 3x L respectively.  

Quantity of P removed by 16L ,

$=\frac{5}{5+3}\times 16\\\\=\frac{5}{8}\times 16\\=5\times2\\=10L$

Quantity of Q removed by 16L ,

$=\frac{3}{5+3}\times 16\\\\=\frac{3}{8}\times 16\\=3\times2\\=6L$

Now, According to question

$\frac{5x-0}{3x-6+16}=\frac{3}{5}$

$25x - 50 = 9x + 30$

$16x = 80$

$x=5$

Now, The quantity of liquid P and Q holds

P=5x=5(5)=25

Q=3x=3(5)=15

Total quantity the vessel hold = 25+15=40 L