Question : A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 2 hours and 20 minutes, the distance is:
Option 1: 35 km
Option 2: 21 km
Option 3: 9 km
Option 4: 12 km
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Correct Answer: 12 km
Solution :
Let the total distance be $x$ km.
2 hr 20 min = 2 + $\frac{1}{3}=\frac{7}{3}$ hr
According to the given condition,
$\frac{x}{12}+\frac{x}{9}=\frac{7}{3}$
⇒ $\frac{3x+4x}{36}=\frac{7}{3}$
⇒ $7x=\frac{7}{3}×36$
⇒ $x=\frac{84}{7}$
$\therefore x= 12$ km
Hence, the correct answer is 12 km.
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