Question

Q. An ornithologist wants to estimate the number of parrots in a large field. She uses a net to catch some, and catches 32 parrots, which she rings and sets free. The following week she manages to net 40 parrots, of which 8 are ringed.

(1) What fraction of her second catch is ringed?
(2) Find an estimate of the total number of parrots in the field.

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Answer 1

Total parrot=40

Caught=8

Fraction

• 8/40
• 1/5

#2

Out of 40 parrots 8 are ringed

Parrots per one ringed=40/8=5

Total ringed before=32

Total no of parrots

• 32(5)
• 160

There are 160 parrots

Answer 2

`\sf 1) \quad (1)/(5)`

`\sf 2) \quad 160\:parrots`

Explanation:

Question 1

Given information:

• Second catch = 40 parrots
• Ringed = 8 parrots

Therefore, the fraction of ringed parrots from the second catch is:

`\implies \sf (ringed\:parrots)/(total\:caught\:parrots)= (8)/(40)=(1 * 8)/(5 * 8)=(1)/(5)`

Question 2

If she caught and ringed 32 parrots in her first catch, but only 1/5 of the parrots caught in the second catch were ringed, then 32 parrots represents 1/5 of the total number of parrots. To find the total number of parrots, simply multiply the total number of ringed parrots by 5:

`\implies \sf \textsf{Total number of parrots}=32 * 5 = 160`