Question
Download Solution PDFA hunter was asked how many birds he had caught and had in his bag. He replied that there were all parrots but eight, all ducks but eight, and all swans but eight. How many birds did he catch in total ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A hunter has birds in his bag. He replied that there were all parrots but eight, all ducks but eight, and all swans but eight.
Formula Used:
Let the number of parrots be P, the number of ducks be D, and the number of swans be S.
From the given conditions:
P + D + S - 8 = P
P + D + S - 8 = D
P + D + S - 8 = S
Calculation:
From the conditions, we can write the following equations:
P + D + S - 8 = P
⇒ D + S = 8
P + D + S - 8 = D
⇒ P + S = 8
P + D + S - 8 = S
⇒ P + D = 8
Adding the three equations:
(D + S) + (P + S) + (P + D) = 3 × 8
⇒ 2P + 2D + 2S = 24
⇒ P + D + S = 12
The total number of birds the hunter caught is 12.
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