Question 14 Marks
Teachers and students of class IX of a school had gone to Nandan Kannan for study tour. After visiting different places of Nandan Kannan, lastly, they visited bird's sanctuary and deer park. Rohan a clever boy and keen observer. He put the question to his friends "How many birds are there and how many deer are there (at particular time) in Nandan Kannan?" Rahul's friend, Nishith gave the correct ansuer us follows:
'Nishith answered that total animals have 1000 eyes and 1400 legs.'
(i) If x and y be the number of birds and deer respectively, what is the equation of total number of eyes?
(a) $x+y=1000$ $\quad$(b) $x+y=500$ $\quad$(c) $x-y=1000$ $\quad$(d) $x-y=500$
(ii) What is the equation of total number of legs?
(a) $2 x+y=70$$\quad$(b) $x+2 y=500$$\quad$(c) $x+2 y=700$$\quad$(d) $2 x-y=500$
(iii) How many birds are there in the Zoo?
(a) 1000 $\quad$(b) 5000 $\quad$(c) 300 $\quad$(d) 200
(iv) How many deer are there in the Zoo?
(a) 500 $\quad$(b) 200 $\quad$(c) 300 $\quad$(d) 700
'Nishith answered that total animals have 1000 eyes and 1400 legs.'
(i) If x and y be the number of birds and deer respectively, what is the equation of total number of eyes?
(a) $x+y=1000$ $\quad$(b) $x+y=500$ $\quad$(c) $x-y=1000$ $\quad$(d) $x-y=500$
(ii) What is the equation of total number of legs?
(a) $2 x+y=70$$\quad$(b) $x+2 y=500$$\quad$(c) $x+2 y=700$$\quad$(d) $2 x-y=500$
(iii) How many birds are there in the Zoo?
(a) 1000 $\quad$(b) 5000 $\quad$(c) 300 $\quad$(d) 200
(iv) How many deer are there in the Zoo?
(a) 500 $\quad$(b) 200 $\quad$(c) 300 $\quad$(d) 700
Answer
View full question & answer→(i) (b): Each bird has two eyes and each deer has also two eyes.
$\therefore \quad \text { Total number of eyes }=2 x+2 y$
But, it is given that the total number of eyes is 1000 .
$\therefore \quad 2 x+2 y=1000 \Rightarrow x+y=500$
(ii) (c): A bird has two legs and a deer has four legs. Therefore, number of legs of $x$ birds and $y$ deer is $2 x+4 y$. It is given that there are 1400 legs.
$\therefore \quad 2 x+4 y=1400 \Rightarrow x+2 y=700$
(iii) (d): We have,
$\quad$$x+y=500$$\quad$...(i)$\quad$ and $x+2y=700$$\quad$...(ii)
Subtgracting (i) from (ii), we obtain
$(x+2 y)-(x+y)=700-500 \Rightarrow y=200$
Putting $y=200$ in (i), we obtain $x=300$. Thus, there are 300 birds.
(iv) (b): From (iii), we obtain $y=200$. Hence, there are 200 deer.
$\therefore \quad \text { Total number of eyes }=2 x+2 y$
But, it is given that the total number of eyes is 1000 .
$\therefore \quad 2 x+2 y=1000 \Rightarrow x+y=500$
(ii) (c): A bird has two legs and a deer has four legs. Therefore, number of legs of $x$ birds and $y$ deer is $2 x+4 y$. It is given that there are 1400 legs.
$\therefore \quad 2 x+4 y=1400 \Rightarrow x+2 y=700$
(iii) (d): We have,
$\quad$$x+y=500$$\quad$...(i)$\quad$ and $x+2y=700$$\quad$...(ii)
Subtgracting (i) from (ii), we obtain
$(x+2 y)-(x+y)=700-500 \Rightarrow y=200$
Putting $y=200$ in (i), we obtain $x=300$. Thus, there are 300 birds.
(iv) (b): From (iii), we obtain $y=200$. Hence, there are 200 deer.