Discussion
In a caravan, in addition to 50 hens there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads, then the number of keepers are:
Answer: C
There are 15 keepers.
Let the number of keepers be k. Hens and keepers have 2 feet, goats and camels have 4, and every member of the caravan has one head.
\[ \begin{aligned} \text{heads} &= 50 + 45 + 8 + k = 103 + k \\ \text{feet} &= 100 + 180 + 32 + 2k = 312 + 2k \end{aligned} \]
\[ \begin{aligned} (312 + 2k) - (103 + k) &= 224 \\ 209 + k &= 224 \\ k &= 15 \end{aligned} \]
Check: with 15 keepers there are 118 heads and 342 feet, and 342 − 118 = 224. The other options give differences of 219, 221 and 227.
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