Deepa rides her bike at an average speed of 30 km/hr and reaches her destination in 6 hours. Hema covers the same distance in 4 hours. If Deepa increases her average speed by 10 km/hr and Hema increases her average speed by 5 km/hr, what would be the difference in their time taken to reach the destination ?

Answer: Option C

Deepa's original speed = 30 km/hr
Deepa's new speed :
= (30 + 10) km/hr = 40 km/hr
Distance = (30 × 6) km = 180 km
Hema's original speed :
= $$\frac{180}{4}$$ km/hr = 45 km/hr
Hema's new speed :
= (45 + 5) km/hr = 50 km/hr
Difference in time :
$$\begin{array}{rl}& =\left(\frac{180}{40}-\frac{180}{50}\right)\text{ hrs}\\ & =\frac{9}{10}\text{ hrs}\\ & =\left(\frac{9}{10}\times 60\right)\text{ min}\\ & =54\text{ min}\end{array}$$