How may litres of water will have to be added to 1125 litres of the `45 %` solution of acid so that the resulting mixture will contain more than `25 %` but less than 30% acid content?

Answer

N/a

Explanation

Let x litres of water be mixed on 1125 liters of 45% acid.
Acid in 1125 litre solution = `(45)/(100)xx1125`
Total mixture = `(1125 + x )` lites
According to the problem,
`25% of (1125 + x) lt (45)/(100)xx1125 lt (1125 + x) 30% of (1125 + x)`
`rArr ((1125 + x )25)/(100) lt (45 xx 1125)/(100) lt ((1125 + x) 30)/(100)`
`rArr (1125 + x) 5 lt 9 xx 1125 lt (1125 + x) 6`
Now, `(1125 + x)5 lt 9 xx1125`
and` 9xx 1125 + lt (1125 + x )6`
`rArr 1125 + x lt 9 xx 225 and 10125 lt 6750 + 6x `
`rArr x lt 900 and x gt 562.5`
`rArr 562.5 lt x lt 900`
Therefore, the required water is more than 562.5 litres and less than 900 litres.