Question

There are 60 hens, 50 goats, 10 camels, and some ducks in a farm. The number of feet of the animals is 270 more than the number of tails. Find the number of ducks in the farm.

• A. 50
• B. 60
• C. 30
• D. 40

Answer 1

The correct option is C 30

Let the number of ducks in the farm be $x$.
Every animal has only one tail.
Total numbers of tails $=60+50+10+x=120+x$

We know a hen has 2 feet, a goat has 4 feet, a camel has 4 feet, and a duck has 2 feet.
Total number of feet = $=60\times 2+50\times 4+10\times 4+x\times 2=120+200+40+2x=360+2x$

Given, the number of feet is 270 more than the number of tails. $\Rightarrow (360+2x)-(120+x)=270$
$\Rightarrow 360-120+2x-x=270$
$\Rightarrow 240+x=270$
$\Rightarrow x=30$
Hence, the number of ducks in the farm is 30.