Question

In the field,there are goats and cocks,total no. of legs is 180 and total no. of eyes is 120,so how many goats and cocks are there in the field? ​

Answer 1

Answer:

30 & 30

Step-by-step explanation:

Let the number of goats be 'a' and cocks be 'b'.

Goats have 4 legs, while cocks have 2 legs, 4 legs of 'a' goats = 4a & 2 legs of 'b' cocks = 2b

Total legs = 4(a) + 2(b)

→ 4a + 2b = 180

→ 2(2a + b) = 2 * 90

→ a + 2b = 90

→ a = 90 - 2b ... (1)

Here, total eyes = 120, as both have 2 eyes, 2 eyes of 'a' goats = 2a & 2 eyes of 'b' cocks = 2b

→ 2a + 2b = 120

→ a + b = 60

→ (90 - 2b) + b = 60 ....{a=90-2b}

→ 90 - b = 60

→90 - 60 = b

→ 30 = b = number of cocks

Therefore,

→ a = 90 - 2b = 90 - 2(30) = 30

→ number of goats = 30