Question

If x ml pure alcohol is added to 400 ml of a 15% solution and after adding its strength becomes 32%, then the value of x is
(A) 50 ml (B) 75 ml
(C) 200 ml (D) 100 ml

Answer 1

\[.15\times 400+x=.32(400+x)\]

Answer 2

both sides representing the total amount of alcohol present

Answer 3

Why .15×400+x=.32(400+x) ?

Answer 4

I didn't understand the question.

Answer 5

x%=x/100
the amount of alcohol in a given mixture is therefor given by the amount of liquid times the percent that is alcohol
so the amount of alcohol in the original mixture is 15% of 400ml, or\[0.15\times400\]good so far?

Answer 6

Yes, I understood

Answer 7

ok, so if we add x ml of PURE alcohol, that is %100 concentration

100% X (ml of new mixture)=100% of x=x ml

So we represent this as\[0.15\times400+1\times x=0.15(400)+x\]i.e. because it is pure alchohol we treat the coefficient of the amount of mixture being added as one.
still good?

Answer 8

Yes

Answer 9

So then we are told our final mixture has 32% alcohol, and the number of milliliters of the substance now is 400+x ml
so the amount of alcohol in our new mixture is then\[0.32(400+x)\]but this must be the same as the amount of alcohol we had before we mixed the two together, which was\[0.15(400)+x\]
so they must be equal

Answer 10

Ok, thanks

Answer 11

100ml