Question

A vessel contains two liquids p and q in the ratio 5:3. If 16l of the mixture is removed and the same quantity of liquid q is added , the ratio becomes 3:5 . What was the quantity of the vessel ? Select one: a. 50 b. 35 c. 45 d. 40

Answer 1

Answer: The quantity of the vessel was

(d) 40l.

The given ratio between p and q is 5:3.

Let the initial quantity of p be 5x and q be 3x

So the total quantity is 8x

After removal of 16l from the mixture and then adding 16l of q:

Net quantity of p= 5x- 10

Net quantity of q= 3x -6 + 16 = 3x + 10

Therefore, the new ratio between p and q =( 5x-10) : (3x+ 10)

According to the given conditions:

( 5x-10) : (3x+ 10) = 3:5

5( 5x-10) = 3(3x+10)

or, 25x -50 = 9x + 30

or, 16x = 80

or, x= 5

So, the quantity of the vessel was = 8x

which is equal to 40l.