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Q.

A group of hens and rabbits have a total of 32 legs. The combined number of hens and rabbits is 12. If the numbers of hens and rabbits are represented by x and y respectively, then express the following pairs of equations to represent the situation? 

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a

x + y = 12 and 2x + 4y = 32 

b

x + y = 12 and 2x + 4y = 22

c

x + y = 10 and 2x + 4y = 12 

d

x + y = 12 and 2x + 4y = 12 

answer is A.

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Detailed Solution

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Number of hens = x 

Number of rabbits = y 

The group has a total of 12 hens and rabbits. 

∴ x + y = 12                       … (1) 

It is known that a hen has 2 legs while a rabbit has 4 legs. 

Thus, the number of legs of hens = 2x 

Similarly, the number of legs of rabbits = 4y 

The hens and rabbits have a total of 32 legs. 

∴ 2x + 4y = 32                   … (2) 

Thus, the required equations to represent the given situation are 

x + y = 12 

2x + 4y = 32 

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