Question

Find the value of $ \dfrac{m}{k} $ if 75% of $ m $ is equal to $ k $ % of 25 where $ k>0 $ .

Answer 1

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} $ .

Complete step-by-step answer:
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.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 1.
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 $ .