Teachers and students of class X of a school had gone to Nandan Kannan for study tour. After visiting different places of Nandan Kannan they visited birds sanctuary and deer park. Rohan is a cleaver 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, Nitish gave the correct answer as follows: Nitish answered that total animals have $1000$ eyes and $1400$ legs. How many birds are there in the zoo?

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Q. Teachers and students of class X of a school had gone to Nandan Kannan for study tour. After visiting different places of Nandan Kannan they visited birds sanctuary and deer park. Rohan is a cleaver 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, Nitish gave the correct answer as follows: Nitish answered that total animals have

1000

eyes and

1400

legs. How many birds are there in the zoo?

Assume Birds and Deer: Let's assume the number of birds is $B$ and the number of deer is $D$ . Birds have $2$ eyes and $2$ legs, deer have $2$ eyes and $4$ legs.
Equations for Eyes and Legs: We have two equations based on the information given: $\newline$ $1$ ) For eyes: $2B + 2D = 1000$ $\newline$ $2$ ) For legs: $2B + 4D = 1400$
Simplify First Equation: Let's simplify the first equation by dividing everything by $2$ : $B + D = 500$
Subtract Equations: Now, let's subtract the simplified first equation from the second equation to find the number of deer: $\newline$ $(2B + 4D) - (B + D) = 1400 - 500$ $\newline$ $B + 3D = 900$
Solve for Deer: We can now solve for $D$ by subtracting $B$ from both sides: $3D = 900 - B$
Substitute and Simplify: Let's substitute $B$ from the first simplified equation ( $B = 500 - D$ ) into the above equation: $\newline$ $3D = 900 - (500 - D)$ $\newline$ $3D = 900 - 500 + D$ $\newline$ $3D = 400 + D$
Solve for D: Now, we solve for D: $\newline$ $3D - D = 400$ $\newline$ $2D = 400$ $\newline$ $D = \frac{400}{2}$ $\newline$ $D = 200$
Find Number of Birds: Now that we have the number of deer, we can find the number of birds by substituting $D$ back into the simplified first equation: $\newline$ $B + 200 = 500$ $\newline$ $B = 500 - 200$ $\newline$ $B = 300$