A man counted his animals, 80 heads and 260 legs (ducks and goats). How many…
2025
A man counted his animals, 80 heads and 260 legs (ducks and goats). How many goats are there ?
- A.
80
- B.
40
- C.
50
- D.
None of these
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Solution: Find the number of goats.
Let the number of ducks be d and the number of goats be g.
Heads give: d + g = 80.
Legs give: 2d + 4g = 260. Divide this equation by 2 to get d + 2g = 130.
Subtract the heads equation from the halved legs equation: (d + 2g) − (d + g) = 130 − 80, so g = 50.
Therefore there are 50 goats. (Check: ducks = 80 − 50 = 30; legs = 2×30 + 4×50 = 60 + 200 = 260.)