If 5 cats can catch 5 mice in 5 minutes, how many cats are needed to catch 100 mice in 100 min?

Correct — A.
Rule: find one cat's rate, then scale.

5 cats catch 5 mice in 5 minutes
So 1 cat catches 1 mouse in 5 minutes.

In 100 minutes, 1 cat catches 100 ÷ 5 = 20 mice.
100 mice ÷ 20 per cat = 5 cats → option (a).

Why the others are wrong

• (b)
  10 — 10 cats catching 20 mice each in 100 minutes take 200 mice, twice the 100 needed.
• (c)
  100 — 100 scales the cats with the mice and ignores the time, which also grew 20-fold. 100 cats would catch 2,000 mice in 100 minutes.
• (d)
  25 — 25 cats catching 20 mice each in 100 minutes take 500 mice, five times the 100 needed.

Work-rate items reduce to one relation: work done = workers × rate × time. Here each cat's rate is 1 mouse per 5 minutes.

The mice and the minutes both grew by the same factor, 20, so the number of cats does not change. Scaling the mice and forgetting the minutes gives 100, option (c).

Key facts

• One cat catches one mouse in 5 minutes.
• In 100 minutes one cat catches 20 mice.
• M₁ × T₁ ⁄ W₁ = M₂ × T₂ ⁄ W₂ gives 5 × 5 ⁄ 5 = x × 100 ⁄ 100, so x = 5.

Common traps

• Answering 100 because the mice rose from 5 to 100, without noticing the time rose by the same factor.

No directly related past PYQ was found.