• # question_answer There are two neighbours, one has 6 oxen and other has 8 cows, and they have common field for the grazing of the cattle. They use the field for their cattle turn wise for feeding them. The 6 oxen or the 8 cows can graze the field in 25 days. In how much time will 1 ox and 2 cows graze the same field if left together? A) 40 days              B)        60 daysC)        50 days               D)        55 daysE) None of these

Explanation Option [b] is correct. According to the question, Time taken by 8 cows = Time taken by 6 oxen. Time taken by 1 cow = Time taken by $\frac{6}{8}$ oxen. Time taken by 2 cows = $\frac{6}{8}\times 2=\frac{3}{2}\,\,oxen\,\,\,\,.$ 1 ox and 2 cows = 1 oxen + $\frac{3}{2}\,$ oxen = $\frac{2+3}{2}$ = $\frac{5}{2}$ oxen. Now, 6 oxen can graze the field in 25 days 1 oxen can graze the field in $25\times ~6=150\text{ }days.$ $\frac{5}{2}$ oxen (1 oxen and 2 cows) can graze the field in $\frac{150}{2.5}~=60\text{ }days$