Question

In certain consignment of eggs. 80 eggs were spoilt in transit. If it constitutes 40% of the total consignment, how many eggs were there in the consignment?

Answer 1

Hint: Let the total quantity of eggs of the consignment be equal to $x$. The value of $x$ can be found out equating 40℅ of $x$ to 80. Write 40% as $\dfrac{{40}}{{100}}$ and of represents multiplication. Then, solve the formed equation, that is , $\dfrac{{40}}{{100}}\left( x \right) = 80$ to find the value of $x$

Complete step by step answer:

Let the total quantity of the eggs in the consignment be equal to $x$.
It is given that 40 percent of the total eggs were spoilt in transit. Also, it is given that the number of eggs spoilt in transit is equal to 80. Therefore the 40 percent of the total eggs is 80.
Subsisting $x$ for the total eggs in the consignment, we get
40% of $x$ is 80.
We can write a given percentage in the form of fractions.
Therefore, 40% is equal to $\dfrac{{40}}{{100}}$
40% of $x$ can be simplified as $\dfrac{{40}}{{100}}$ of $x$
Now, we know that it represents multiplication.
Hence the above expression is $\dfrac{{40}}{{100}}\left( x \right)$
Also, we are given that 40% of $x$ is equal to 80 eggs.
Therefore, $\dfrac{{40}}{{100}}\left( x \right) = 80$
On simplifying the above expression, we get,
$0.4x = 80$
Dividing the equation throughout by 0.4
$
  x = \dfrac{{80}}{{0.4}} \\
   \Rightarrow x = \dfrac{{800}}{4} \\
   \Rightarrow x = 200 \\
$
Thus the total quantity of eggs in the consignment is equal to 200.

Note: Percentage is the ratio that represents as a fraction of 100. A percent can be written as a decimal or a fraction. Here, we have solved questions by simplifying the value $\dfrac{{40}}{{100}}$ as 0.4 and then solving it. We can also do it by cross-multiplying and then solving for the value of $x$