How many litres of water have to be added to 1125 litres of 45% acid solution, so that the resulting mixture contains more than 25% but less than 30% acid content?
Answers
Answer:
Let's add x litres of water
Now if the solution is 45% acid then it is 55% water.
Equating water in initial and final solution, When solution is 25% acid:
x+0.55(1125)=0.75(x+1125)
x+618.75=0.75x+843.75
0.25x=225
x=900 (to get 25% of acidic solution)
Equating water in initial and final solution, When solution is 30% acid:
x+0.55(1125)=0.7(x+1125)
x+618.75=0.7x+787.5
0.3x=168.75
x=562.5 (to get 30% of acidic solution)
i.e 562.5<x<900
Answer:
Let x litre of water is required to be added
Then, total mixture =(x+1125) litres
It is evident that the amount of acid contained in the resulting mixture is 45% of 1125 litres.
This resulting mixture will contains more than 25% but less than 30% acid content.
∴30% of (1125+x)>45% of 1125
And, 25% of (1125+x)<45% of 1125
⇒
100
30
(1125+x)>
100
45
×1125
⇒ 30(1125+x)>45×1125
⇒ 30×1125+30x>45×1125
⇒ 30>45×1125−30×1125
⇒ 30x>(45−30)×1125
⇒ x>
30
15×1125
=562.5
25% of (1125×x)<45% of 1125
⇒
100
25
(1125+x)<
100
45
×1125
⇒ 25(1125+x)>45×1125
⇒ 25×1125+25x>45×1125
⇒ 25x>45×1125−25×1125
⇒ 25x>(45−25)×1125
⇒ x>
25
20×1125
=900
∴562.5<x<900
Thus, the required number of litres of water that is to be added will have to be more than 562.5 but less than 900.