Question

A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six and all ducks but six. How many birds had he in all?
A. 9
B. 18
C. 27
D. 19

Answer 1

Hint: In order to find the number of birds in the bag first assume the number of birds, sparrow, pigeon and ducks in terms of some unknown variable. Then use the problem statement in order to convert the entire unknown variable into one variable and find some equation. And finally solve the equations.

Complete step by step answer:

Let us consider the number of all birds in the bag is x.
Also let us consider:
Number of sparrows = s
Number of pigeons = p
Number of ducks = d
Given problem statement is: there were all sparrows but six, all pigeons but six and all ducks but six.
So let us conclude the number of each bird from the statement.
All sparrows but six $ \Rightarrow s = x - 6$
All pigeons but six $ \Rightarrow p = x - 6$
All ducks but six $ \Rightarrow d = x - 6$
Now we know the number of each bird and also the total number of birds.
Total number of birds = Number of sparrows + Number of pigeons + Number of ducks
$
   \Rightarrow x = s + p + d \\
   \Rightarrow x = \left( {x - 6} \right) + \left( {x - 6} \right) + \left( {x - 6} \right) \\
 $
Now, let us solve the equation in order to find the value of x.
$
   \Rightarrow x = 3x - 18 \\
   \Rightarrow 3x - x = 18 \\
   \Rightarrow 2x = 18 \\
   \Rightarrow x = \dfrac{{18}}{2} \\
   \Rightarrow x = 9 \\
 $
Hence, the shooter had 9 birds in the bag.

So, option A is the correct option.

Note: In order to solve these types of problems with complex problem statements, it is first and foremost important to understand the statement and infer some conclusion from it. It is easier to solve the practical problem as above if converted to an algebraic problem.