Question

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, find the number of keepers.

• A. $15$
• B. $16$
• C. $17$
• D. $19$

Answer 1

The correct option is A $15$

Let $x$ be the number of keepers.

Total number of heads of $50$ hens, $45$ goats ,$8$ camels and $x$ keepers =$50+45+8+x=103+x$

Total number of legs of $50$ hens =$100$

Total number of legs of $45$ goats =$180$

Total number of legs of $8$ camels =$32$

Total number of legs of $x$ keepers =$2x$

Total legs = $100+180+32+2x=312+2x$
Total number of feet is $224$ more than $312+2x$

$\therefore$ $103+x=312+2x-224$

$\therefore$ $x=15$