Ten cows can graze in a field for 15 days and twenty cows can graze in the same field for 10 days. For how many days can 30 cows graze in the field?
Answers
30 cows graze in the field for 15/2 days
Given:
Ten cows can graze in a field for 15 days
Twenty cows can graze in the same field for 10 days
To Find:
For how many days can 30 cows graze in the field?
Solution:
Note: Here grass grow daily also and there is initial grass also
Step 1:
Assume initial grass = x , grows daily = y , and grass a cow graze daily = z
Step 2:
Calculate how much grass 10 cows graze in 15 days
10*15*z = x + 15y
=> 150z = x + 15y Eq1
Step 3:
Calculate how much grass 20 cows graze in 10 days
20*10z = x + 10y
=> 200z = x + 10y Eq2
Step 4:
Eq1 - Eq2
-50z = 5y
=> y = -10z
Step 5:
Substitute y = -10z in Eq1
150z = x + 15(-10z)
=> x = 300z
Step 6:
Calculate how much grass 30 cows graze in d days
30*d*z = x + dy
Substitute x = 300z and y = -10z
30dz = 300z + d(-10z)
=>40dz = 300z
=> d = 300/40
=> d = 15/2
Hence 30 cows graze in the field for 15/2 days