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Question
How many 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?
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Solution
Let x litres 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 contain more than 25% but less than 30% acid content.
∴ 30% of (1125 + x) > 45% of 1125
And, 25% of (1125 + x) < 45% of 1125
30% of (1125 + x) > 45% of 1125
⇒ `30/100 (1125 + x) > 45/100 xx 1125`
⇒ 30 (1125 + x) > 45 x 1125
⇒ 30 x 1125 + 30 x > 45 x 1125
⇒ 30x > 45 x 1125 - 30 x 1125
⇒ 30 x > (45 -30) x 1125
⇒ `x > (15 xx 1125)/30 = 562.5`
25% of (1125 + x) < 45% of 1125
⇒ 251001125 + x < 45100 × 1125
⇒ 251125 + x < 45 × 1125
⇒ 25 × 1125 + 25x < 45 × 1125
⇒ 25x < 45 × 1125 -25 × 1125
⇒ 25x < 22500
⇒ x < 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.
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