In a courtyard there are chickens and goats. Heads counted = 100; legs counted = 320. Find the number of chickens and goats.

Introduction / Context:
This is a standard heads-and-legs puzzle. With two types of animals, each with a known number of legs (2 for chickens, 4 for goats), we can set up two linear equations to find the exact counts given total heads and total legs.

Given Data / Assumptions:

• Chickens (2 legs), goats (4 legs).
• Total heads = 100.
• Total legs = 320.

Concept / Approach:
Let c = chickens, g = goats. Then c + g = 100 and 2c + 4g = 320. These two linear equations uniquely determine c and g.

Step-by-Step Solution:
c + g = 100 … (1) 2c + 4g = 320 ⇒ divide by 2 ⇒ c + 2g = 160 … (2) Subtract (1) from (2): g = 60 ⇒ c = 100 − 60 = 40.

Verification / Alternative check:
Legs check: 40 chickens * 2 = 80 legs; 60 goats * 4 = 240 legs; total = 320, matching the data.

Why Other Options Are Wrong:
20,50 totals only 70 heads; 30,70 yields 320 legs but 100 heads? (30+70=100) but legs 30*2 + 70*4 = 60 + 280 = 340 (too high). 50,50 gives 300 legs (too low).

Common Pitfalls:
Solving with trial instead of equations can lead to errors. Using simultaneous equations ensures correctness.

Final Answer:
40 , 60