Two numbers are, respectively, 28% and 25% less than a third number. What percent is the first number of the second number?

Concept Used:

The percentage is a way of comparing the quantities. Suppose, 20 number is x% of y. Then, the relation between x and y can be given as,

\(\dfrac{x}{100}\times y=20\)

Explanation:-

Suppose that the three numbers are x, y and z.

Here, x is 28% less than z. Thus,

\(\begin{aligned} &\Rightarrow \mathrm{x}=(100-28)\% \text { of } \mathrm{z}\\ &\Rightarrow \mathrm{x}=\frac{72}{100} \times \mathrm{z}=0.72 \mathrm{z} \end{aligned}\)

Also, y is 25% less than z. Thus,

\(\begin{aligned} &\Rightarrow \mathrm{y}=(100-25)\% \text { of } \mathrm{z}\\ &\Rightarrow \mathrm{y}=\frac{75}{100} \times \mathrm{z}=0.75 \mathrm{z} \end{aligned}\)

So, the percent first number of the second number,

\(\begin{aligned} &P\%=\frac{y}{x} \times 100 \%\\ &P\%=\frac{0.72 \mathrm{z}}{0.75 \mathrm{z}} \times 100 \%\\ &P\%=0.96 \times 100 \%\\ &P\%=96\% \end{aligned}\)

Thus, 96% is the first number of the second number.

Hence, the correct option is 1.