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Manav has a collection of $1300$ stamps, $65\%$ of the stamps are Indian stamps while the rest of foreign stamps. Find the number of Indian and foreign stamps in his collection.

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Last updated date: 20th Jun 2024
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Answer
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Hint: The collection possessed by Manav consists of the stamps which are of two categories; the Indian stamps and the foreign stamps. We can let the respective numbers of these to be equal to $x$ and $y$. Since the total stamps in the collection is equal to $1300$, so the sum of $x$ and $y$ will be equal to $1300$, which can be mathematically expressed as an equation. Also, $65\%$ of the total stamps are the Indian stamps, which means that $65\%$ of the total $1300$ stamps is equal to $x$. From this we can find the value of $x$ which can be substituted in the equation formed above to get the value of $y$, the number of foreign stamps.

Complete step by step solution:
Let the number of Indian stamps in his collection be $x$ and that of the foreign stamps be $y$. Since the total number of stamps is equal to $1300$, so we can write
$\Rightarrow x+y=1300........(i)$
Now, according to the question, $65\%$ of the total $1300$ stamps are Indian stamps, which means that
$\begin{align}
  & \Rightarrow x=\dfrac{65}{100}\times 1300 \\
 & \Rightarrow x=65\times 13 \\
 & \Rightarrow x=845 \\
\end{align}$
Substituting this in (i) we get
$\begin{align}
  & \Rightarrow 845+y=1300 \\
 & \Rightarrow y=1300-845 \\
 & \Rightarrow y=455 \\
\end{align}$
Hence, the number of the Indian and the foreign stamps are equal to \[845\] and \[455\] respectively.

Note: We need not form the equation $x+y=1300$ but can separately determine the respective number of stamps. The calculation for the Indian stamps is already shown in the solution. And since the total percentage is always equal to $100$, so the percentage of the foreign stamps will be equal to $\left( 100-65 \right)$, or $35$ percentage of the total $1300$. From this we can calculate the number of foreign stamps too.