Question 1202921
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Dhruv bought some white sugar and some brown sugar. 
He used an equal amount of white and brown sugar. 
He had 3/5 of the while sugar and 1/2 of the brown sugar left. 
What fraction of the sugar which Dhruv bought was used?
(1) 4/7
(2) 4/9
(3) 5/11
(4) 7/10
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<pre>
Let  "w"  be the amount of the white sugar Dhruv bought.

Let  "b"  be the amount of the brown sugar Dhruv bought.


He used  {{{(2/5)w}}}  and  {{{(1/2)b}}}.


From the problem, we have this equation

    {{{(2/5)*w}}} = {{{(1/2)*b}}}    ("He used an equal amount of white and brown sugar"),

or  0.4*w = 0.5*b.                         (1)


They want you calculate this ratio  

    {{{(0.4*w + 0.5*b)/(w+b)}}}.                       (2)


From (1), express  w = {{{(0.5/0.4)*b}}} = 1.25*b  and substitute it into (2).  You will get

   {{{(0.4*w + 0.5*b)/(w+b)}}} = {{{(0.4*1.25b + 0.5*b)/(1.25b+b)}}} = {{{(0.5b+0.5b)/(2.25b)}}} = {{{b/(2.25b)}}} = {{{1/2.25}}} = {{{1/((9/4))}}} = {{{4/9}}}.


<U>ANSWER</U>.  The fraction of the sugar Dhruv used was  {{{4/9}}}  of the total amount of the sugar.
</pre>

Solved.