Question

$6$ oxen or $8$ cows can gaze a field in $28$ days. How long would $9$ oxen and $2$ cows take to graze the same field?

• A. $16$ days
• B. $20$ days
• C. $15$ days
• D. $25$ days

Answer 1

Answer: (A)

$16$ days

$6$ oxen $=8$ cows
$1$ oxen $=\frac{8}{6}$ cows
$9$ oxen $=\frac{8}{6}\times 9$ cows $=12$ cows
$\left(\begin{array}{c}9\text{oxen}+2\text{cows}\end{array}\right)\equiv \left(\begin{array}{c}12\text{cows}+2\text{cows}\end{array}\right)=14\text{cows}$
Now, $8$ cows can graze the field in $28$ days
$1$ cow can graze the field in $\left(\begin{array}{c}28\times 8\end{array}\right)$ days
$14$ cows can graze the field in $\frac{28\times 8}{14}$ days $=16$ days.