Question

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?

• A. 90
• B. 95
• C. 92
• D. 99

Answer 1

The Correct Option is B

Let's solve this problem using algebra:

1. Define Variables:

• Let 'd' be the number of ducks.
• Let 'r' be the number of rabbits.

2. Set Up Equations:

• Heads: Each animal has one head, so d + r = 160.
• Legs: Ducks have 2 legs, and rabbits have 4 legs, so 2d + 4r = 450.

3. Solve the Equations:

• From the first equation, we can express 'r' in terms of 'd': r = 160 - d.
• Substitute this expression for 'r' into the second equation: 2d + 4(160 - d) = 450.
• Simplify: 2d + 640 - 4d = 450.
• Combine like terms: -2d = 450 - 640.
• -2d = -190.
• d = -190 / -2.
• d = 95.

4. Find the Number of Rabbits (Optional):

• r = 160 - d = 160 - 95 = 65

5. Answer:

• The number of ducks in the zoo is 95.

The correct answer is Option 2.