Question

 A person spent Rs 564 in buying geese and ducks. If each goose costs Rs 7, each duck Rs 3, and if the total number of birds bought was 108, how many of each did he buy?
(a) 60 and 48
(b) 48 and 36
(c) 48 and 24
(d) 60 and 30

Answer 1

Hint: In order to solve this problem, we need to develop two-equations having two unknowns. We can get one condition by the total number of birds bought by the person and we can get the second equation from the condition of the total money spent on buying these birds. Then we need to solve these equations simultaneously and get the answer.

Complete step-by-step answer:
We have a person who needs to buy two types of birds namely goose and duck.
The cost of each goose is Rs 7 and the cost of each duck is Rs 3.
Let the number of geese that the person buy be $x$ .
Let the number of ducks that the person buy be $y$ .
According to the first condition, we have the total birds that the person bought are 108.
Therefore, we can say that,
$x+y=108..............(i)$
Let's move on with the second condition.
The total money spent on buying these birds are Rs 564.
From the above assumption, we can see that the cost of $x$ geese will be $\text{=Number of geese }\!\!\times\!\!\text{ cost of each goose}$ .
Therefore, the cost of $x$ the geese is $7x$ .
Similarly, the assumption we can see that the cost of $y$ duck will be $\text{=Number of ducks }\!\!\times\!\!\text{ cost of each duck}$ .
Therefore, the cost of $y$ the ducks is $3y$ .
As we already know that the total cost is Rs 564.
The equation formed is as follows,
$7x+3y=564........................(ii)$
We have two equations (i) and (ii) and two unknowns
Multiplying equation (i) by 3 we get,
$\begin{align}
  & 3x+3y=108\times 3=324 \\
 & 3x+3y=324...................(iii) \\
\end{align}$
Subtracting equation (iii) from equation (ii), we get,
$\begin{align}
  & \,\,\,\,\,7x+3y=564 \\
 & \dfrac{-\left( 3x+3y=324 \right)}{4x+0y=240} \\
\end{align}$
Solving for $x$ , we get,
$x=\dfrac{240}{4}=60...................(iv)$
Substituting the value of $x$ in equation (i), we get,
$60+y=108$
Solving for $y$ , we get,
$y=108-60=48.................(v)$
From (iv) and (v), we get
The person buys 60 geese and 48 ducks.
Hence, option (a) is the correct option.

Note: We can get the answers by a different approach as well. We know that the total number of birds bought is 108. Therefore, we can just try out the option and the option that give the summation to be 108 will be the correct option. As we can see that option (b), (c), (d) are already eliminated as they don’t sum up to 108. Hence, we can say that option (a) is the correct option.