Question 121

# It was a rainy morning in Delhi when Rohit drove his mother to a dentist in his Maruti Alto. They started at 8.30 AM from home and Rohit maintained the speed of the vehicle at 30 Km/hr. However, while returning from the doctor’s chamber, rain intensified and the vehicle could not move due to severe water logging. With no other alternative, Rohit kept the vehicle outside the doctor’s chamber and returned home along with his mother in a rickshaw at a speed of 12 Km/hr. They reached home at 1.30 PM. If they stayed at the doctor’s chamber for the dental check-up for 48 minutes, the distance of the doctor’s chamber from Rohit’s house is

Solution

Let $$x$$(in km) be the distance from the home to the clinic
Thus, the time taken to reach the clinic = $$\dfrac{x}{30}$$ hours
They stay at the clinic for $$\dfrac{48}{60} = \dfrac{4}{5}$$ hours
The time taken to reach home from clinic = $$\dfrac{x}{12}$$ hours
Total time = 5 hours
Thus, $$\dfrac{x}{30}+\dfrac{4}{5}+\dfrac{x}{12}$$ = $$5$$
=> $$\dfrac{2x}{60}+\dfrac{48}{60}+\dfrac{5x}{60}$$ = $$5$$
Thus, $$300 = 7x+48$$
Thus, $$x=36$$
Hence, the doctor's clinic is 36 kms away.
Hence, option C is the correct answer.

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