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Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

a) 2 : 5
b) 3 : 5
c) 4 : 5
d) 6 : 7

Answer: c
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{third}}\,{\text{number}}\,{\text{be}}\,x \cr & {\text{Then,}}\,{\text{first}}\,{\text{number}} \cr & = 120\% \,{\text{of}}\,x = \frac{{120x}}{{100}} = \frac{{6x}}{5} \cr & {\text{Second}}\,{\text{number}} \cr & = 150\% \,{\text{of}}\,x = \frac{{150x}}{{100}} = \frac{{3x}}{2} \cr & {\text{Ratio}}\,{\text{of}}\,{\text{first}}\,{\text{two}}\,{\text{numbers}} \cr & = {\frac{{6x}}{5}:\frac{{3x}}{2}} = 12x:15x = 4:5 \cr} $$

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