The circumferences of the front and rear wheels of a bicycle are 3.5 m and 3 m respectively. If the vehicle is moving at a speed of 15 m/sec, the shortest time in which both the wheels will make a whole number of turns is :

Solution(By Examveda Team)

Time taken by front wheel to complete one revolution :
$$\eqalign{ & = \left( {\frac{{3.5}}{{15}}} \right)\sec \cr & = \frac{7}{{30}}\operatorname{sec} \cr} $$
Time taken by rear wheel to complete one revolution :
$$\eqalign{ & = \left( {\frac{3}{{15}}} \right)\sec \cr & = \frac{1}{5}\sec \cr} $$
∴ Required time :
$$\eqalign{ & = \left[ {{\text{L}}{\text{.C}}{\text{.M}}{\text{. of }}\frac{7}{{30}}{\text{and}}\frac{1}{5}} \right]\sec \cr & = \left( {\frac{{{\text{L}}{\text{.C}}{\text{.M}}{\text{. of 7 and 1}}}}{{{\text{H}}{\text{.C}}{\text{.F}}{\text{. of 30 and 5}}}}} \right)\sec \cr & = \frac{7}{5}\sec \cr & = 1.4\,\sec \cr} $$