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Last updated date: 26th Nov 2023
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# Find the value of $\dfrac{m}{k}$ if 75% of $m$ is equal to $k$ % of 25 where $k>0$ .

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Hint: We first use the percentage values on particular numbers. We get the equation of proportionality. We use that to find the simplified form of $\dfrac{m}{k}$ .

We know for any arbitrary percentage value of a%, we can write it as $\dfrac{a}{100}$ . The percentage is to find the respective value out of 100.
Therefore, 75% and $k$ % can be written as $\dfrac{75}{100}$ and $\dfrac{k}{100}$ .
Now we need to find the 75% of $m$ which is equal to $m\times \dfrac{75}{100}=\dfrac{3m}{4}$ .
Then we need to find the $k$ % of 25 which is equal to $25\times \dfrac{k}{100}=\dfrac{k}{4}$ .
These two forms are equal which gives the impression of $\dfrac{3m}{4}=\dfrac{k}{4}$ .
We need to find the simplified form of $\dfrac{m}{k}$ from the above equation.
For the fraction $\dfrac{x}{y}$ , we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{x}/{}_{d}}{{}^{y}/{}_{d}}$ .
For the equation $\dfrac{3m}{4}=\dfrac{k}{4}$ , we get $\dfrac{m}{k}=\dfrac{4}{4\times 3}=\dfrac{1}{3}$ . Therefore, the value of $\dfrac{m}{k}$ is $\dfrac{m}{k}=\dfrac{1}{3}$ .
So, the correct answer is “ $\dfrac{1}{3}$ ”.
Note: We need to be careful about the cross-multiplication and finding the GCD of the simplification. Both of the numbers get divided by that GCD to find the ratio of $m$ and $k$ .