Probability Examples 1

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Q. In a field, there are some ducks and goats. The total number of heads is 77 and the total number of legs is 224. How many ducks are there ?

(A) 35 (B) 42 (C) 45 (D) 40

Solution:

Duck = 2 legs
Goat = 4 legs

1st: Find extra legs

If all 77 animals were ducks: 77 × 2 = 154

Extra legs: 224 − 154 = 70

2nd: Find goats

Each goat has 2 extra legs: 70 ÷ 2 = 35

So,

Goats = 35

3rd: Find ducks : 77 − 35 = 42 

Ans: (B) 42 Ducks

Shortcut

Goats = 224 − (77×2) / 4−2 = 70/2 = 35 , Ducks = 77−35 = 42

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Q. A pen has 40 heads and 112 legs. All the animals are cows and chickens. How many cows are there ?

A) 12  B) 16  C) 20  D) 24

​Solution:

Given:

• Total heads = 40 means Total animals = 40


• Total legs = 112


• Cow = 4 legs


• Chicken = 2 legs

1st: Assume all 40 animals are chickens.

40 × 2 = 80 legs

2nd: Find the extra legs.

112 − 80 = 32 extra legs

3rd: A cow has 2 more legs than a chicken.

Number of cows = 32 ÷ 2 = 16

4th: Find the chickens.

40 − 16 = 24 chickens

Check

16 cows × 4 = 64 legs
24 chickens × 2 = 48 legs

Total legs = 64 + 48 = 112

Ans: B) 16

Formula:

Cows = (Total Legs − 2 × Total Animals) ÷ 2

= (112 − 80) ÷ 2
= 16

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