Question

A mixture contains a and b in the ratio 5:9 . 14 litres of this mixture is taken out and 14 litres of b is poured in. Now the ratio of a to b becomes 2:5 . Find the amount of b originally present un the mixture

Answer 1

this is the solution

Answer 2

Answer:

45 litres.

Step-by-step explanation:

Let the quantity of 'a' initially in the mixture was 5x litres and that of 'b' was 9x litres.

So, the quantity of the mixture was (5x+9x)= 14x litres.

Now, 14 litres of mixture is taken out in which 5 litres was 'a' and 9 litres was 'b'.{ In ratio 5:9}.

Hence, the new quantity of the mixture is (14x-14) litres in which (5x-5) litres is 'a' and (9x-9) litres is 'b'.

Now, we add 14 litres of 'b' in the mixture.

Hence, the new quantity of the mixture is again 14x litres in which (5x-5) litres is 'a' and (9x-9+14) =(9x+5) litres is 'b'.

The ratio of 'a' and 'b' in the new mixture is given to be 2:5.

Hence, we can write that, $\frac{5x-5}{9x+5} =\frac{2}{5}$

⇒ 25x-25 =18x+10

⇒ 7x=35

⇒ x=5

Therefore, amount of 'b' originally present in the mixture  was 9x =9×5 = 45 litres. (Answer)