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 in the caravan, find the number of keepers.
A. 5
B. 8
C. 10
D. 15

Answer 1

Hint: Here, we will first find the total number of heads and the total number of feet. After that we will try to form an equation according to the given condition. Solving that linear equation, will give the answer.

Complete step-by-step answer:
Let us assume that the total numbers of keepers are = x
It is given that number of hens = 50
Number of goats = 45
Number of camels = 8
Since, we know that a hen has two feet, a goat has 4 feet and a camel has 4 feet.
So, the total number of feet of hens = $50\times 2=100$
Total number of feet of goats = $45\times 4=180$
Total number of feet of camel =$8\times 4=32$
Since, each keeper will have 2 feet. So, the total number of feet of keepers =$2x$
Therefore, the total number of feet in the caravan will be:
= 100 + 180 + 32 + 2x
= 312 + 2x
Also, the total number of heads in the caravan will be:
= x + 50 + 45 + 8
=103 + x
According to the question, the total number of feet in the caravan is 224 more than the number of heads in the caravan. So, we can write the following equation:
312 +2x = 103 + x +24
312 + 2x = 327 + x
2x – x = 327-312
X = 15
So, the value of x comes out to be 15.
Hence, the total number of keepers in the caravan is 15.

Note: While solving this problem, students should correctly write the number of feet each of the animals have and also the number of feet of a keeper. Confusion in the number of feet may lead to mistakes. Also, the equations should be made correctly to avoid unnecessary mistakes.