15 lts are taken of from a container full of liquid a and replaced with liquid b. again 15 more lts of the mixture is taken and replaced with liquid b. after this process, if the container contains liquid a and b in the ratio 9: 16, what is the capacity of the container h?	Pick.
A) a : 45
B) b : 25
C) c : 37.5
D) d : 36
E) e : 42
<gadget id="calculator">9 + 16</gadget>
<output>25</output>

<gadget id="calculator">9 / 25</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) ** (1/2)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">15 / (2/5)</gadget>
<output>75/2 = around 37.5</output>

<result>C</result>
15 lts are taken of from a container full of liquid a and replaced with liquid b. again 15 more lts of the mixture is taken and replaced with liquid b. after this process, if the container contains liquid a and b in the ratio 9: 16, what is the capacity of the container h?
divide(15, subtract(const_1, sqrt(divide(9, add(9, 16)))))
if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct .