Question

A container has a mixture of two liquids P and Q in the ratio 7:5. When 9 litres of mixture are drawn off and the container is filled with Q, the ratio of P and Q becomes 7: 9. How many litres of liquid P was contained in the container initially? a) 21 b) 63 c) 35 d) 28 e) 14 1 20.
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Answer 1

Answer:

Step-by-step explanation:

Let the total amount of solution be x lit.

The ratio of P and Q in 9 lit will be same as in the main solution.

So amount of P in 9 lit. = ( 9×7)/ 12

= 21/4 lit

So, amount of Q in 9 lit = (9×5)/12

= 15/4 lit

The initial amount of P is= 7x/12

The initial amount of Q is= 5x/12

After drawing out and adding on the amount of P In the new solution = 7x/12 - 21/4

=( 7x - 63)/ 12

Amount of Q in new solution = 5x/12 - 15/4 +9

= (5x + 63)/ 12

So the equation is,

(7x - 63)/12 : (5x + 63)/12 = 7:9

Or,( 7x - 63)/ (5x + 63) = 7/9

Or, 63x - 567 = 35x + 441

Or, 28x = 1008

Or, x= 36 lit

So amount of P is= (36×7)/12 = 21 lit