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# Find $x$ in the following: $x:5 = 10:50$

Last updated date: 18th Mar 2023
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Hint: First we have to define what the terms we need to solve the problem are.
Since ratio is the comparison of any two or more that two terms of quantities of the same kind by solving or dividing is referred as the ratio. And the use of it gives or shows how many times or compared one quantity is equal to one another or some more quantities.

As per the given question we need to find the unknown value $x$ from the ratio of $x:5 = 10:50$
Since as we see $x$ is the only unknown value and all other terms are known we simply solve by ratio comparison or by division.
Let us able to write the given question as per division, $x:5 = 10:50 \Rightarrow \dfrac{x}{5} = \dfrac{{10}}{{50}}$ (rewriting the ratio as respect to division so that cancelling the given terms yields the unknown factor)
Now we are going to apply the division formula of $\Rightarrow \dfrac{x}{5} = \dfrac{{10}}{{50}} \Rightarrow \dfrac{x}{5} = \dfrac{1}{5}$ (in right hand side equation the ten and fifty will cancels each other and resultant)
Thus, we get by the cross multiplying the terms we have $\Rightarrow \dfrac{x}{5} = \dfrac{1}{5} \Rightarrow 5x = 5$
Since the right-hand side five is equal to the left-hand side five $x$ thus cancelling the common terms, we get. $\Rightarrow 5x = 5 \Rightarrow x = 1$
Therefore $x = 1$ is the required thing in the ratio $x:5 = 10:50$
Note: We can also able to solve the required ratio by simplifying terms like $x:5 = 10:50$ which yields as $x$ is equal to ten and then five is equal to fifty so that cancelling on five and fifty, we get the same ten which $x$ has before; hence x has cancelled that ten with right side values and therefore we get $x = 1$