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Question

A manufacturer has 460 litres of a 9% acid solution. How many litres of a 3% acid solution must be added to it so that the acid content in the resulting mixture be more than 5% but less than 7%?


Solution

Let x litres of a 3% arid solution be added to 460 litres of 9% acid solution. Then, 

total quantity of mixture = (460 +x) litres. 

Total acid content in (460 + x)litres of mixture

={(460×9100)+(x×3100)}litres=(2075+3x100) litres. 

Now, the add content in the resulting mixture must be more than 5% and less than 7%. 

 5% of (460+x)<(2075+3x100)<7% of (460+x)

 5100×(460+x)<4140+3x100<7100×(460+x)

 5(460+x)<4140+3x<7(460+x)

 2300+5x<4140+3x<3220+7x

 2300+5x<4140+3x and 4140+3x<3220+7x

 5x3x<41402300 and 41403220<7x3x

 2x<1840 and 920<4x

 x<920 and 230<x

 230<x<920.

Hence, the required quantity of 3% acid solution to be added must be more than 230 litres and less than 920 litres.

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