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's assume that Dhruv initially bought 10 units of sugar (to keep the calculations simple).
Since he used an equal amount of white and brown sugar, he used 3/5 * 10 = 6 units of white sugar and 1/2 * 10 = 5 units of brown sugar.
Therefore, a total of 6 + 5 = 11 units of sugar were used.
Since Dhruv initially bought 10 units of sugar, the fraction of sugar used is 11/10 = 11/10 * 1/1 = 11/10.
But this fraction is greater than 1, which does not make sense. Therefore, our initial assumption of 10 units of sugar is incorrect.
Let's try a different assumption.
Let's assume Dhruv initially bought 15 units of sugar.
He used an equal amount of white and brown sugar, so he used 3/5 * 15 = 9 units of white sugar and 1/2 * 15 = 7.5 units of brown sugar.
Since we cannot have half units of sugar, let's assume Dhruv rounded down and used only 7 units of brown sugar.
Therefore, a total of 9 + 7 = 16 units of sugar were used.
Since Dhruv initially bought 15 units of sugar, the fraction of sugar used is 16/15.
This fraction cannot be simplified further, so the answer is (4) 16/15, which is not one of the given answer choices.
Therefore, none of the provided answer choices is correct.
Let's assume that Dhruv bought a total of x amount of sugar.
He used an equal amount of white and brown sugar, so he used (1/2)x amount of each.
Dhruv had 3/5 of the white sugar left, which means he used 1 - 3/5 = 2/5 of the white sugar.
Similarly, he had 1/2 of the brown sugar left, which means he used 1 - 1/2 = 1/2 of the brown sugar.
To find the fraction of the sugar Dhruv used, we need to add the amounts of white and brown sugar he used and divide it by the total amount of sugar.
So the fraction of sugar used is ((2/5)x + (1/2)x) / x = (4/10 + 5/10) = 9/10.
Therefore, the correct answer is option (4) 7/10.