Q9 of 32 Page 107

A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?

Let the x litres of 3% solution is to be added to 460 liters of the 9% of solution, then


Total solution = (460 + x) litres


Total acid content in resulting solution



= (41.4 + 0.03x)%


It is given that resulting mixture should be more than 5% acidic but less than 7% acidic


⇒ 5 % of (460 + x) < 41.4 + 0.03x < 7% of (460 + x)



⇒ 23 + 0.05 x < 41.4 + 0.03x < 32.2 + 0.07x


Now, we have


⇒ 23 + 0.05x < 41.4 + 0.03x and 41.4 + 0.03x < 32.2 + 0.07x


⇒ 0.02x < 18.4 and 0.04x > 9.2


⇒ 2x < 1840 and 4x > 920


⇒ x < 920 and x > 230


⇒ 230 < x < 920


Hence, solution must be added between 230 l and 920 l


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