Question : A man has some hens and some cows. If the total number of heads of both is 50 and the number of feet of both is 142, then the number of cows is:
Option 1: 21
Option 2: 25
Option 3: 27
Option 4: 29
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Correct Answer: 21
Solution :
Let's assume:
h = number of hens
c = number of cows
From the problem, we can make two equations:
1) Each hen and each cow has one head:
h + c = 50 ––(i)
2) Each hen has 2 feet and each cow has 4 feet:
2h + 4c = 142 ––(ii)
From equation (i), we can express h in terms of c:
h = 50 – c ––(iii)
Now, substituting the value of h from equation (iii) into equation (ii), we get:
2(50 – c) + 4c = 142
⇒ 2c = 142 – 100
⇒ c = $\frac{42}{2}$
⇒ c = 21
Hence, the number of cows is 21.
Option 1 is correct.
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