How to buy 100 birds for Rs 100 if 4 hens costs Rs 1, 1 parrot for Rs 4 and 1 rooster for Rs 7?

Question

40 Hen for Rs 1
1 pigeons for Rs 3
1 rooster for Rs 5

How to buy 100 birds for Rs 100?

Answer 1

1. 88 hens, 2 parrots, 10 roosters (88+2+10=100, 22+8+70=100)
2. 84 hens, 11 parrots, 5 roosters (84+11+5=100, 21+44+35=100)

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x- hen,
y- parrot,
z- rooster
1) x+y+z=100
2) 0.25x+ 4y+ 7z=100-->x+16y+28z=400
if subtract 1) from 2) we get 15y+27x=300-->5y+9z=100,
we get 2 answers: y=2, z=10, then x=88 or y=11, z=5 and x=84