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%?

A manufacturer has 460 litres of a 9%acid solution. How many litres of

1.	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%?
Answer» Solution :Let x LITRES of a 3% acid 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 `={(460xx(9)/(100))+(x xx (3)/(100))}"litres"=((207)/(5)+(3x)/(100))`litres. Now, the acid content in the resulting mixture must be more than 5% and less than 7%. `therefore5%of(460+x)lt((207)/(5)+(3x)/(100))lt7% "of"(460+x)` `rArr(5)/(100)xx(460+x)lt(4140+x)/(100)lt(7)/(100)xx(460+x)` `rArr5(460+x)lt4140+3xlt7(460+x)` `rArr 2300+5xlt4140+3xand 4140+3xlt3220+7x` `rArr 5x=3xlt4140-2300 and 4140+3x lt3220 +7x` `rArr2xlt1840and 920 lt4x` `rArr xlt920and 230ltx` `rArr 230ltxlt920` Hence, the REQUIRED quantity of 3% acid solution to be added must be more than 230 litres and less than 920 litres.