In the Delhi zoo, there are some ducks and rabbits. If the heads are counted, there are 160, while the legs are 450. What will be the number of ducks in the zoo?

Question

Accepted Answer

Let the number of **ducks** be $$ x $$ and the number of **rabbits** be $$ y $$.

#### Step 1: Formulate Equations
1. Total heads:  
   $$ x + y = 160 $$

2. Total legs:  
   Ducks have 2 legs, and rabbits have 4 legs:  
   $$ 2x + 4y = 450 $$

#### Step 2: Simplify Equation (2)
Divide equation (2) by 2:  
$$
x + 2y = 225 
$$

#### Step 3: Solve Simultaneous Equations
Subtract equation (1) from equation (3):  
$$
(x + 2y) - (x + y) = 225 - 160.
$$  
Simplify:  
$$
y = 65.
$$

Substitute $$ y = 65 $$ into equation (1):  
$$
x + 65 = 160.
$$  
Solve for $$ x $$:  
$$
x = 160 - 65 = 95.
$$

#### Step 4: Verify the Solution
- Total heads: $$ x + y = 92 + 65 = 160 $$ ✅  
- Total legs: $$ 2x + 4y = (2 	imes 95) + (4 	imes 65) = 190 + 260 = 450 $$ ✅

Thus, the number of ducks is **95**.

Answer

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