In a pet shop, there are only parrots and rabbits. Total heads = 40, and total legs = 100. How many parrots are there?

Correct — C.
Rule: assume every animal is a parrot, then turn the missing legs into rabbits.

If all 40 were parrots: 40 × 2 = 80 legs
Legs still missing: 100 − 80 = 20
Each rabbit adds 4 − 2 = 2 legs, so rabbits = 20 ÷ 2 = 10

Parrots = 40 − 10 = 30 → option (c).
Check: 30 × 2 + 10 × 4 = 60 + 40 = 100 legs.

Why the others are wrong

• (a)
  20 — 20 parrots leaves 20 rabbits: 20 × 2 + 20 × 4 = 40 + 80 = 120 legs, 20 too many.
• (b)
  25 — 25 parrots leaves 15 rabbits: 25 × 2 + 15 × 4 = 50 + 60 = 110 legs, 10 too many.
• (d)
  35 — 35 parrots leaves 5 rabbits: 35 × 2 + 5 × 4 = 70 + 20 = 90 legs, 10 too few.

Two kinds of animal and two totals give two equations. With r rabbits and 40 − r parrots, the legs give 2(40 − r) + 4r = 100, so 80 + 2r = 100 and r = 10.

The assume-all method is the same algebra done in your head. Alligation works too: 100 legs over 40 heads is 2.5 legs a head, so parrots : rabbits = (4 − 2.5) : (2.5 − 2) = 3 : 1, which is 30 parrots.

Key facts

• Parrots have 2 legs and rabbits 4, so each rabbit in place of a parrot adds 2 legs.
• Heads count the animals: parrots + rabbits = 40.
• 30 parrots and 10 rabbits give 60 + 40 = 100 legs.

Common traps

• Stopping at 10, the rabbits, when the question asks for parrots
• Dividing the 100 legs by 4 as if every animal were a rabbit, which gives 25

No directly related past PYQ was found.