To solve the problem given, let's first understand the statement:
If \(x\%\) of \(a\) is equal to \(y\%\) of \(b\), then mathematically it can be represented as:
\(\frac{x}{100} \times a = \frac{y}{100} \times b\)
By simplifying, we can find the relation between \(a\) and \(b\) as:
\(\Rightarrow x \times a = y \times b\)
\(\Rightarrow a = \frac{y}{x} \times b\)
Now, we need to find what percent of \(a\) is \(z\%\) of \(b\).
Let's express \(z\%\) of \(b\):
\(\frac{z}{100} \times b\)
We now need to find what percent this quantity is of \(a\).
Using the relation between \(a\) and \(b\) from above:
\(\Rightarrow a = \frac{y}{x} \times b\)
Thus, the percentage of \(a\) is given by
\(\frac{\left(\frac{z}{100} \times b\right)}{\left(\frac{y}{x} \times b\right)} \times 100 = \frac{zx}{y}\)
Therefore, the correct answer is \(\frac{zx}{y}\).
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
