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 number of ducks in the zoo ?
The correct answer is
95
Delhi Zoo Ducks and Rabbits Calculation
Let $d$ represent the number of ducks and $r$ represent the number of rabbits in the Delhi zoo.
Formulating Equations
Based on the information provided:
- Total heads: The sum of ducks and rabbits is 160. $d + r = 160$
- Total legs: Ducks have 2 legs and rabbits have 4 legs. The total number of legs is 450. $2d + 4r = 450$
Solving the Equations
We can solve this system of linear equations. First, express $r$ in terms of $d$ from the heads equation:
$r = 160 - d$Now, substitute this expression for $r$ into the legs equation:
$2d + 4(160 - d) = 450$Simplify and solve for $d$:
$2d + 640 - 4d = 450$ $640 - 2d = 450$Isolate the term with $d$:
$2d = 640 - 450$ $2d = 190$Calculate the number of ducks:
$d = \frac{190}{2}$ $d = 95$Result
Therefore, the number of ducks in the zoo is 95.
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Important Questions from Simplification (Notes)
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Identify the number that will replace the question mark in the second equation based on the relationship represented in the first equation.
- Simplify $(5z-12y)^2 + (12z+5y)^2 - 144z^2$.
- Simplify: $[(36 + 4 \times (3 + 2 \times (5 - 2))) \div (6 + 3)] + [(40 - (6 + 3 \times 2)) + (8 \times 2 - 6)]$
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