The lowest temperature in the night in a city is one third more than $$\frac{1}{2}$$ the highest during the day. Sum of the lowest temperature and the highest temperature is 100 degrees. Then what is the lowest temperature?

Solution(By Examveda Team)

Let the highest temperature be x degrees
Then, lowest temperature
$$\eqalign{ & {\text{ = }}\left[ {\left( {1 + \frac{1}{3}} \right)\frac{x}{2}} \right]{\text{ degrees }} \cr & = \left( {\frac{4}{3} \times \frac{x}{2}} \right){\text{ degrees}} \cr & = \frac{{2x}}{3}{\text{ degrees}} \cr & \therefore x + \frac{{2x}}{3} = 100 \cr & \Leftrightarrow \frac{{5x}}{3} = 100 \cr & \Leftrightarrow x = \frac{{100 \times 3}}{5} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 60 \cr & {\text{So, lowest temperature}} \cr & {\text{ = }}\left( {\frac{2}{3} \times 60} \right){\text{degrees}} \cr & {\text{ = 40 degrees}} \cr} $$