No Options..please help

[reply2spg]

Forty liters of a 60% salt solution are reduced to a 45% solution. How much must be drained off and replaced with distilled water to that the resulting solutions will contain only 45% salt?

[touche]

soln......vol.......salt......water
6o%.....40 .......24........16
end reqmt
45%......40.......18........22
to reduce 6 of salt drain this
60%.......10........6.........4
bal soln is
60%.......30.......18.......12
add 10 litres dist water and get end reqmt

[Attack]

Consider for 100g of solution we have 60g salt and 40g water.
we need only 45g or salt per 100g solution. ie 15 grams of salt has to be drained out.
so we need to drain 25 g of solution to eliminate 15 g of salt (60:100 :: 15:25), and replace it with distilled water.


hence for 40l of solution we need to drain out 10l of solution and replace that with distilled water

[muralik]

let x be the liters removed

remaining salt content = (40-x)*60/100


adding x liters of distilled water

40-x +x = total content
salt content/total content = 45/100

45/100 = (40-x)*0.6/40

(40-x)/40 = 45/60
1- x/40 = 3/4

x/40 = 1/4
x =10

hope this helps

[Fiver]

An easier way to solve this mentally:
current volume of salt is 60%=24 needs to be reduced to 45%=18
6 liters of salt to be reduced corresponds to 10 liters of the solution, as salt is 60% of the solution.

[finsisher]

Originally Posted by touche

soln......vol.......salt......water
6o%.....40 .......24........16
end reqmt
45%......40.......18........22
to reduce 6 of salt drain this
60%.......10........6.........4
bal soln is
60%.......30.......18.......12
add 10 litres dist water and get end reqmt

at times drawing makes life very easy well done Touche

[clock60]

one more way
40*0.6=24-salt
let it be x liters of solution need to drain to obtain 45% solution
(24-0,6*x)/40=0,45
24-0,6x=0,45*40
0,6x=6
x=10

[arindambanerji]

40 lts of salt soln

60% of salt = 24
water = 40% = 16

now 45% of x = 24
x=480/9

now to make it whole number, we need a salt concentration that could result x*100/45 to a whole number…so the nearest possible value is 18

so reduce the salt concentration by 6
and the water has to be 22 lits to make the 45% soln hence add 6lts of water..

but other results are possible as well…not an authentic question..

[arindambanerji]

Originally Posted by touche

soln......vol.......salt......water
6o%.....40 .......24........16
end reqmt
45%......40.......18........22
to reduce 6 of salt drain this
60%.......10........6.........4
bal soln is
60%.......30.......18.......12
add 10 litres dist water and get end reqmt

I think the question is asking to replace the salt by water..which means we will have to add water..isnt it?

so whould it not be 6 lts the amount of water added after replacing 6 kg of salt from the solution ....to make it 22 from 16?

"How much must be drained off and replaced with distilled water "

[touche]

Originally Posted by arindambanerji

I think the question is asking to replace the salt by water..which means we will have to add water..isnt it?

so whould it not be 6 lts the amount of water added after replacing 6 kg of salt from the solution ....to make it 22 from 16?

"How much must be drained off and replaced with distilled water "

implies originAL solution
the question is clear!