Question

2 cows and 7 calves can graze a field in 14 days. 3 cows and 8 calves can graze the same field in 11 days. Then 8 cows and 6 calves can graze 4 times the same field in how many days? It is known that, once grazed; the grass does not grow back

• A. 21
• B. 281
• C. 392
• D. 18

Answer 1

The correct option is C

392

Aàcows
Bàcalves
2 cows and 7 calves are needed to do a piece of work in 14 days. This means to complete the work we need 2 cows to graze for 14 days and 7 calves to graze for 14 days. So if we want to complete the work in one day we need: $2\times \left(14\right)=28$ cows and $7\times \left(14\right)=98$ calves $\Rightarrow$ 28A + 98B.
Also, 3 cows and 8 calves take 11 days, so if they need to complete the work in 1 day, we need 3(11) =33 cows and 8 (11) =88 calves $\Rightarrow$ 33A + 88B
We can now equate the two cases as 28A + 98B = 33A + 88B
Solving we get 5A=10B or 1A=2B
i.e. one cow is equivalent to two calves.
We need to calculate for 8 cows $\&$ 6 calves or 8+3=11 cows
3 cows and 8 calves can graze the field in 11 days $\Rightarrow$ 7 cows can graze the field in 11 days
$\Rightarrow$ 11 cows can graze the field in 7 days

Thus, 11 cows can graze 4 fields in 7 $\times$ 4=28 days. Option (d)