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?
- 90
95
92
- 99
The Correct Option is B
Solution and Explanation
To find the number of ducks in the zoo, we use the given information: There are 160 heads and 450 legs. Let the number of ducks be \(d\) and the number of rabbits be \(r\). Since each duck and rabbit has one head, we have the equation:
\(d + r = 160\)
Each duck has 2 legs and each rabbit has 4 legs. Thus, the second equation is:
\(2d + 4r = 450\)
We can simplify the second equation by dividing it by 2:
\(d + 2r = 225\)
Now, we have the system of equations:
\(1. \quad d + r = 160\)
\(2. \quad d + 2r = 225\)
Subtract equation 1 from equation 2:
\((d + 2r) - (d + r) = 225 - 160\)
\(r = 65\)
Substitute \(r = 65\) back into equation 1:
\(d + 65 = 160\)
\(d = 160 - 65\)
\(d = 95\)
Therefore, the number of ducks in the zoo is 95.
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