6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in:

24 days

The correct answer is Option (3) → 24 days

Let the work done = 1 field.

If 6 goats graze it in 50 days:

$6G×50=1⇒G=\frac{1}{300}$ (field per day)

Similarly, 8 sheep graze it in 50 days:

$8S×50=1⇒S=\frac{1}{400}$ (field per day)

Rate for 8 goats and 6 sheep

Work rate = $8G+6S$

Substitute values:

$8\left(\frac{1}{300}\right) + 6\left(\frac{1}{400}\right)$

Find common denominator = 1200:

$=\frac{8 \times 4}{1200} + \frac{6 \times 3}{1200}$

$=\frac{32 + 18}{1200} = \frac{50}{1200} = \frac{1}{24}$

$\text{Time taken} = \frac{\text{work}}{\text{rate}}$

Time = $\frac{1}{1/24} = 24$ days