A millionaire bought a lot of hats $\frac{1}{4}$ of which were brown. The millionaire sold $\frac{2}{3}$ of the hats including $\frac{4}{5}$ of the brown hats. What fraction of the unsold hats were brown?
(a)$\frac{1}{60}$ $\frac{1}{2}$
(b)$\frac{1}{15}$ $\frac{2}{3}$
(c)$\frac{3}{20}$ $\frac{3}{4}$
(d)$\frac{3}{5}$ $\frac{2}{7}$
(e)$\frac{3}{4}$ 287. Equal amounts of water were poured into two empty jars of different capacities, which made one jar $\frac{1}{4}$ full and the other jar $\frac{1}{3}$ full. If the water in the jar with lesser capacity is, then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water? (M.A.T., 2005)
Answer
Answer (as printed): C
Explanation
Let the number of hats purchased be x. Then, number x of brown hats = . 4 QUANTITATIVE APTITUDE 2x Number of hats sold = . Number of hats left unsold 3 2x x = x − = . 3 3 4 x x Number of brown hats sold = of = . Number of 5 4 5 x x x brown hats left unsold = – = . 4 5 20 x 20 = x × 3 = 3 . \ Required fraction = x 20 x 20 3
Explanation as extracted from the printed page; notation may be imperfect.