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, the number of keepers is

Options

A. 5
B. 8
C. 10
D. 15

Answer

D

Explanation

Let the number of Keepers = x
Then, total number of feet
`= 2 xx 50 + 4 xx 45 + 4 xx 8 + 2x `
`= 2x + 100 + 180 + 32 = 2x + 312 `
[`because` Hen = 2 legs, Goat = 4 legs, Camel = 4 legs and Keeper = 2 legs]
And total number of heads = `50 + 45 + 8 + x = 103 + x `
[`because` Hen = Goat = Camel = Keeper `implies` One Head]
According to the question,
`(2x + 312)= (103 + x) + 224 `
or, `x= 327 - 312 `
or, `x= 15 `
So, Required number of keepers = `x = 15`.