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

Let amount of white and brown bought, be W and B, respectively
As {{{3/5}}} of white (W) remained, he used {{{2/5}}} of the white (W), or {{{2W/5}}}
As {{{1/2}}} of brown (B) remained, he used {{{1/2}}} of the brown (B), or {{{B/2}}}
Since the same amount of white and brown was used, then we get: {{{matrix(1,3, 2W/5, "=", B/2)}}}
                                                                 5B = 4W ------ Cross-multiplying 
                                                                 {{{matrix(1,3, B, "=", 4W/5)}}}
Total amount used: {{{matrix(1,7, 2W/5 + B/2, "=", 2W/5 + (4W/5)/2, "=", 2W/5 + 2W/5, "=", 4W/5)}}}
 Total amount bought: {{{matrix(1,7, W + B, "=", W + 4W/5, "=", (5W + 4W)/5, "=", 9W/5)}}} 
  Fraction of total amount bought thatw's used: {{{highlight_green(matrix(1,7, (4W/5)/(9W/5), "=", (4W/5)(5/(9W)), "=", (4cross(W)/cross(5)) * (cross(5)/(9cross(W))), "=", highlight(4/9)))}}}</pre>