Question

) a can contains a mixture to two liquids. a and b in the ratio 7:5, when 9 litres of mixture are drawn off and the can is filled with b, the ratio of a and b becomes 7:9. how many litres of liquid a was contained by the can initially

Answer 1

It is given that ratio of a:b is 7:5

So, 7x litres of liquid ‘a’ and 5x litres of liquid ‘b’ are present

Therefore total parts = 7+5 = 12 parts

When we take out 9 litres of liquid mixture,

Amount of liquid ‘a’ removed will be: (7/12) * 9

Amount of liquid ‘b’ removed will be: (5/12) * 9

Now, 9 litres of liquid ‘b’ is added to the can and new ratio is 7:9

New mixture:

Amount of liquid ‘a’ in new mixture will be: 7x – [(7/12) * 9] = 7x – 5.25

Amount of liquid ‘b’ in new mixture will be: 5x – [(5/12) * 9] + 9 = 5x + 5.25

New ratio:

(7x – 5.25) / (5x + 5.25) = 7/9

63x – 36.75 = 35x + 47.25

28x = 84

x=3

Amount of ‘a’ in original mixture = 7x = 21 litres