Two numbers are respectively 20% and 50% of a third number. What per cent is the first number of second?

110%
220%
330%
440%

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let third number is x . \\ Then first no . \\ 20 % of x = \frac{20 x}{100} \\ Second number \\ = 50 % of x = \frac{50 x}{100} \\ Percent of first no of second no, \\ = [\frac{(\frac{20 x}{100})}{(\frac{50 x}{100})}] \times 100 \\ = \frac{(2 \times 100)}{20} \\ = 40 % \end{aligned}

$\eqalign{ & {\text{Let third number is x}}. \cr & {\text{Then}}\,{\text{first}}\,{\text{no}}{\text{.}} \cr & 20\% \,{\text{of}}\,x = \frac{{20x}}{{100}} \cr & {\text{Second}}\,{\text{number}} \cr & = 50\% \,{\text{of}}\,x = \frac{{50x}}{{100}} \cr & {\text{Percent of first no of second no,}} \cr & = \left[ {\frac{{\left( {\frac{{20x}}{{100}}} \right)}}{{\left( {\frac{{50x}}{{100}}} \right)}}} \right] \times 100 \cr & = \frac{{\left( {2 \times 100} \right)}}{{20}} \cr & = 40\% \cr}$