Question : 10 horses can graze a field in 14 days, and 10 sheep take 28 days to graze the same field. How many days will 5 horses and 10 sheep take to graze the same field?
Option 1: 28
Option 2: 10
Option 3: 14
Option 4: 20
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Correct Answer: 14
Solution :
Number of days in which 10 horses can graze a field = 14 days
Number of days in which 10 sheep can graze a field = 28 days
Efficiency = $\frac{\text{Total Work Done}}{\text{Total Time Taken}}$
Number of days taken by 5 horses to graze a field = 14 × 2 = 28 days
According to the question,
10 sheep can graze a field in 28 days
So, 5 horses = 10 sheep
Efficiency of 1 horse = efficiency of 2 sheep
The total time taken by 5 horses and 10 sheep to graze a field means,
Total = 10 + 10 = 20 sheep
Therefore, the total time taken by 20 sheep to graze the field = $28\times \frac{10}{20}$ = 14 days
$\therefore$ 5 horses and 10 sheep can graze the field in 14 days.
Hence, the correct answer is 14 days.
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