1.

A man when asked 'how many hens and buffaloes he has ?'. He replied that they have 78 eyes and 110 legs in all. Find the number of hens and buffaloes separately.

Answer» Let the number of hens = x
and the numbers of buffaloes = y
We know that, hen as well as buffalo has 2 eyes while hen has 2 legs and buffalo has 4 legs.
So, according to the problem,
2x + 2y = 78 implies x + y = 39 …(1)
Also, 2x + 4y = 110 implies x + 2y = 55 ...(2)
Subtracting equation (1) from (2), we get
y = 16
Putting y = 16 in equation (1), we get
x + 16 = 39 implies x = 23
`therefore` Number of hens = 23 and number of buffaloes = 16


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