Question

At a farm, there are hens, cows and bullocks, and keepers to look after them. There are 69 heads less than legs; the number of cows is double of that of bullocks; the number of cows and hens is the same and there is one keeper per ten birds and cattle. The total number of hens plus cows and bullocks and their keepers does not exceed 50. How many cows are there?

• A. 10
• B. 12
• C. 14
• D. 16

Answer 1

The Correct Option is B

Let the number of hens = h, cows = c, bullocks = b, keepers = k.
Also given, h = c and c = 2b \(==>\) h = c = 2b
Also given is k = \(\frac{(h+c+b)}{10}\) , substituting from above relations, we have k = \(\frac{b}{2}\)
Now, adding up the total living beings: h + c + b + k <= 50 which implies 5.5b \(<= \)50
Adding up for the number of the legs: 2h + 4c + 4b + 2k <= 119 which implies b \(<=\) 7
If we take b = 7, then k = 3.5 which is not possible
If we take b = 6, k = 3 and h = c = 12 each
Hence, number of cows = 12